Previous to the origins of the stars and life as we know it, there was the Galaxy Cauldron. It was a magical, warm place filled with a welcoming light that brought hope. From it, life is born in the form of star seeds.
There used to be a time when light and dark were one and the same in the Cauldron, but this changed once life itself began. Seeds destined to light were created and separated from the darkness. Some of these seeds released a light stronger than the rest. These will be known as Sailor Crystals, which are star seeds that contain great power.

While this was happening, a large explosion was happening in the rest of the universe which originated an infinity of galaxies, planets, asteroids and more. All seeds are destined to a certain planet, and when this planet is created, the seeds begin their travel to them.
The most powerful Sailor Crystal in the universe went to the Moon, accompanied by a lot other star seeds. One of them followed it from afar, its glow was weak and gray.
When the Silver Crystal, the name of the mentioned Sailor Crystal, arrived to its destiny, it started to shine with a bright pink light which took the shape of a female human. She was and adult woman, long silver hair with a slight lavender tone to it. Even though she was naked, an energy field coming from her crystal was protecting her.

Before her eyes, countless white sparkles appeared leaving being a small sky blue eyed woman, her white hair decorated with pearls around it, and crossing her forehead as well. She also worn a necklace of the same material, and a dress that took on a round shape from her hips. Holding with her left hand a staff that had a shining ball on its top.

“Who are you?” the silver haired woman asked.

“My name is Guardian Cosmos,” she answered. “I’m the protector of the Galaxy Cauldron, the place where you were born, and I also guard the Cosmos Crystal. Now that life has begun all around universe, my duty is to guide stars like you to fulfill their mission.”

“Mission?”

“Yes. Your name is Serenity, you possess the Sailor Crystal that protects this star, the Moon. Your mission is to protect it. If an evil being ever threatens the peace of this place, you must use the power of your star seed to vanquish it.”

“And what about these star seeds?”

“With the power of your Silver Crystal, you can make them turn into humans as well, and you can also use your power to create a kingdom in which these stars can live,” she informed Serenity.

Serenity nods to let Cosmos know she understands.

“It is important as well that both you and the inhabitants of the Moon, watch over the evolution of human beings in that blue planet you can see in the sky called Earth, and guide them in the good path. Do you think you’ll be able to fulfill both these missions?”

“Yes, I will.”

“Good, I must go now. As you know, there are many other stars like you that need guidance to help maintain the peace of the universe. I wish you luck, goodbye,” Guardian Cosmos said, releasing a white light that faded along with her.

Once she vanished away from her sight, the Silver Crystal appeared before her, so she took it in her hands. She focused on what Cosmos said, and the crystal emitted a golden light that spread itself through the Moon. Because of this power, the Silver Millennium was created and the star seeds were able to become human beings and automatically recognized her as their queen.

“Welcome to our kingdom, the Silver Millennium. I’m Queen Serenity, I will be the ruler of this kingdom, and together we will fulfill a very important mission. Please, look up to the sky. Can you see that blue planet over there?” she said.

The people of the kingdom do as Serenity says, and in fact find the planet she just mentioned.

“We were given the mission to take care of it from this place and guide its people. I hope you can help me with this task.”

“Of course,” the people responded all at once.

By the end of this reunion, Queen Serenity and the rest of the people celebrated the beginning of the Silver Millennium by throwing a party in which everyone met each other. In the middle of it, Serenity went to a balcony to watch the Earth, wondering what the future holds for her.
 

Blake wrote:

Previous to the origins of the stars and life as we know it, there was the Galaxy Cauldron. It was a magical, warm place filled with a welcoming light that brought hope. From it, life is born in the form of star seeds.

There used to be a time when light and dark were one and the same in the Cauldron, but this changed once life itself began. Seeds destined to light were created and separated from the darkness. Some of these seeds released a light stronger than the rest. These will be known as Sailor Crystals, which are star seeds that contain great power.

Maybe reconsider the order of the statements - talk about what happened before life formed, and then after, for a better flow. This talks about life, then goes back to where there was no life, and mentions life starting, which jostles the reader just a bit   

Quote :

While this was happening, a large explosion was happening in the rest of the universe which originated an infinity of galaxies, planets, asteroids and more. All seeds are destined to a certain planet, and when this planet is created, the seeds begin their travel to them.

The most powerful Sailor Crystal in the universe went to the Moon, accompanied by a lot other star seeds. One of them followed it from afar, its glow was weak and gray.

Perhaps change that first sentence so 'was happening' doesn't repeat itself in the same sentence. For instance, "While the seeds of life grew in the Cauldron, a large explosion erupted through the universe, originating an infinity of galaxies, planets, asteroids, and more."  Also, perhaps "a planet" or "their planet" rather than 'this planet', and 'the seed begins' rather than 'the seeds begin'; just noun/verb stuff.

And maybe instead of "accompanied by a lot other star seeds," just "accompanied by other star seeds" or a specific number; "a lot" suggests a vague concept and can distract the reader with background thoughts ((a lot of other star seeds? Like how many? ten? twenty? thirty thousand?)) while what you want them to take away from the sentence is more along the lines of "Moon is super powerful, and a little grey star seed followed" and get them wondering about that little grey starseed. 

Quote :

When the Silver Crystal, the name of the mentioned Sailor Crystal, arrived to its destiny, it started to shine with a bright pink light which took the shape of a female human. She was and adult woman, long silver hair with a slight lavender tone to it. Even though she was naked, an energy field coming from her crystal was protecting her.

"When that most powerful Crystal, the Silver Crystal, reached its destination," maybe? 
I like how you described Queen Serenity forming, but maybe combine sentences to make it flow a little better? Like throw in 'adult' with 'female human', and then go on to describe her silver hair. I'm not sure if "even though" works with the naked business - it kinda reads that typically her energy field wouldn't protect her if she were naked, which I don't think is what you're going for xD 

Quote :

Before her eyes, countless white sparkles appeared [and disappeared? where did the sparkles go that they then left behind the guardian?] leaving being a small sky-blue eyed woman, her white hair decorated with pearls around it, and crossing [her hair? what crosses her forehead? the pearls?]her forehead as well. She also worn a necklace of the same material[pearls? Maybe make pearls a main feature and then go on to list where they are in her attire?], and a dress that took on a round shape from her hips. Holding with her left hand a staff that had a shining ball on its top.

^^' I had a few questions here with sentence structure, but I put the questions in there for you.

Quote :

“Who are you?” the silver haired woman asked.

“My name is Guardian Cosmos,” she ["the small woman" maybe? "she" could lead the reader into interpreting that silver-haired woman answered he own question] answered. “I’m the protector of the Galaxy Cauldron, the place where you were born, and I also guard the Cosmos Crystal. Now that life has begun all around universe, my duty is to guide stars like you to fulfill their mission.”

“Mission?”

“Yes. Your name is Serenity, you possess the Sailor Crystal that protects this star*, the Moon. Your mission is to protect it. If an evil being ever threatens the peace of this place, you must use the power of your star seed to vanquish it.”

*Maybe instead of "star", this "System"? or this "moon" or "celestial body"? When "Star" is used in Sailor Moon, it typically identifies with a person, a soul, or an actual star like Sol. 
With "protect", maybe change one to an adjective so the word isn't so close together in the same paragraph? Such as "the Sailor Crystal that guards this ____"; as 'protect' works wonderfully in the next bit. 

Quote :

“And what about these star seeds?”

“With the power of your Silver Crystal, you can make them turn into humans as well, and you can also use your power to create a kingdom in which these stars can live,” she informed Serenity.

*yes, good use of 'stars' in this bit. ^^

Quote :

Serenity nods to let Cosmos know she understands.

“It is important as well that both you and the inhabitants of the Moon, watch over the evolution of human beings in that blue planet you can see in the sky called Earth, and guide them in the good path. Do you think you’ll be able to fulfill both these missions?”

“Yes, I will.”

“Good, I must go now. As you know, there are many other stars like you that need guidance to help maintain the peace of the universe. I wish you luck, goodbye,” Guardian Cosmos said, releasing a white light that faded along with her.

Does Serenity know that already? Is it to be an inherent knowledge? It kinda sounds assumptive on Cosmos's part, especially as she just told Serenity that Serenity can pretty much make up her own human companions, and then went on that Earth will have life that Serenity has to protect, while Earth wouldn't be protecting itself. o_o idk what I'm going on about; tldr "As you know" might not be the best phrase to use when talking to someone who just popped into being XD

Quote :

Once she vanished away from her sight, the Silver Crystal appeared before her, so she took it in her hands. She focused on what Cosmos said, and the crystal emitted a golden light that spread itself through the Moon. Because of this power, the Silver Millennium was created and the star seeds were able to become human beings and automatically recognized her as their queen.

“Welcome to our kingdom, the Silver Millennium. I’m Queen Serenity, I will be the ruler of this kingdom, and together we will fulfill a very important mission. Please, look up to the sky. Can you see that blue planet over there?” she said.

I think that if they automatically recognized her as their queen, you could make this statement a little more elegant on Queen Serenity's behalf; she wouldn't have to introduce herself or her position.

This welcome message will be very important to your interpretation of Serenity, as her personality can develop here in just a few short lines, so I'll leave rephrasing to you, should you choose to rephrase it.   

Quote :

The people of the kingdom do as Serenity says, and in fact find the planet she just mentioned.

“We were given the mission to take care of it from this place and guide its people. I hope you can help me with this task.”

“Of course,” the people responded all at once.

By the end of this reunion, Queen Serenity and the rest of the people celebrated the beginning of the Silver Millennium by throwing a party in which everyone met each other. In the middle of it, Serenity went to a balcony to watch the Earth, wondering what the future holds for her.

I didn't catch all of them in there, but you do want to watch your verb tenses - a lot of this is in the past tense and then flashes to the present and back.    Just choose a narrative position and stick with it!

There used to be a time when light and dark were one and the same, but this changed once life itself began in the Galaxy Cauldron. It was a magical, warm place filled with a welcoming light that brought hope.

From this place, life was born as star seeds, which were meant for light and were immediately separated from the darkness. Some of these seeds released a light, brighter and stronger than the rest. These were known as Sailor Crystals, which are seeds that contain great powers. The star seeds had to stay in the Cauldron for a very long time. This happened because, after the seeds were born, the rest of the universe was created.

When all the galaxies, including their planets, asteroids, stars and more, that were meant to receive life were created, the seeds left the Cauldron to begin their journey to their respective homes.

The most powerful Sailor Crystal in the universe went to the Moon, accompanied by other star seeds. One of them followed it from afar, its glow was weak and gray.

When the Silver Crystal, the name of the mentioned Sailor Crystal, arrived to its destination, it started to shine with a bright pink light which took the shape of an adult female human. She was a woman, long silver hair with a slight lavender tone to it. With no clothes on, an energy field coming from her crystal was protecting her.

Before her eyes, countless white sparkles appeared leaving behind a small sky blue eyed woman, her white hair was decorated with pearls, worn as a headband and crossing her forehead as well. She also worn a necklace of the same material, and a dress that took on a round shape from her hips. Holding with her left hand a staff that had a shining ball on its top.

“Who are you?” the silver haired woman asked.

“My name is Guardian Cosmos,” the small woman answered. “I’m the protector of the Galaxy Cauldron, the place where you were born, and I also guard the Cosmos Crystal. Now that life has begun all around universe, my duty is to guide stars like you to fulfill their mission.”
“Mission?”

“Yes. Your name is Serenity, you possess the Sailor Crystal that guards this celestial body, the Moon. Your mission is to protect it. If an evil being ever threatens the peace of this place, you must use the power of your star seed to vanquish it.”

“And what about these star seeds?”

“With the power of your Silver Crystal, you can make them turn into humans as well, and you can also use your power to create a kingdom in which these stars can live,” she informed Serenity.

Serenity nods to let Cosmos know she understands.

“It is important as well that both you and the inhabitants of the Moon, watch over the evolution of human beings in that blue planet you can see in the sky called Earth, and guide them in the good path. Do you think you’ll be able to fulfill both these missions?”

“Yes, I will.”

“Good, I must go now. There are many other stars like you that need guidance to help maintain the peace of the universe. I wish you luck, goodbye,” Guardian Cosmos said, releasing a white light that faded along with her.

Once she vanished away from her sight, the Silver Crystal appeared before her, so she took it in her hands. She focused on what Cosmos said, and the crystal emitted a golden light which formed the Moon Castle, and quickly spread its way through the Moon, creating homes for the star seeds. The power of the crystal helped them become human beings.

Serenity dressed herself in a white dress and added a subtle small pearl decoration to her forehead, which ended in her crescent moon mark. She also dressed the people in white with her magic, and they immediately recognized her as their queen.

“Welcome to our kingdom, the Silver Millennium. I’m Serenity. Together we will fulfill a very important mission. Please, look up to the sky. Can you see that blue planet over there?” she said.

The people of the kingdom do as Serenity said, and in fact they find the planet she just mentioned.
“We were given the mission to take care of it from this place and guide its people. I hope you can help me with this task.”

“Of course,” the people responded all at once.

By the end of this reunion, Queen Serenity and the rest of the people celebrated the beginning of the Silver Millennium by throwing a party in which everyone met each other. In the middle of it, Serenity went to a balcony to watch the Earth, wondering what the future holds for her.

For a reason that couldn’t be explained as anything but destiny making its own way, the gray star seed drifted away from the rest, with a few followers of its own. This star seed turned into a black haired teenage girl, thanks to the power of the Silver Crystal. She looked at the kingdom from a distance, slightly jealous of its beauty.

She wished to live in a palace like that one, and the moment she turned her back and it was in front of her, she realized Serenity wasn’t the only one who possessed powers.