"A raven cawed before flying from a leafless tree as a young girl walked through the woods."
That is a very strong first sentence, starting with something happening immediately.
"This girl wore a blank coutenance as she continued forward. She had long black hair tied in uneven twintails, the left one being longer than the right. She also had sapphire blue eyes and pale skin. She wore an all black outfit consisting of a bikini top under a jacket, tight fitting shorts, knee high boots and long gloves. A sword called Black Blade was sheathed on her right hip. She is also able to summon a large gun called Rock Cannon."
I'd actually say that's about the right amount of detail that can be memorized, so again good job not overloading but still painting a picture.
"As Black Rock Shooter walked, she looked around herself. She sensed some strange and strangely familiar presences within the vicinity. She would soon emerge into a clearing. The Other Self gazed up at the sky for a few moments and took in the sight of the clear night sky, the countless stars that dotted it, and the full moon that hovered in it. When she looked back down, she let out a shocked gasp at what faded into view. A train station. In the middle of a forest. And waiting to leave that station was none other than the Phantom Train."
Still strong and leaving me looking for something to complain about but I'm not finding it. You are conveying good show not tell so we see things as would your character rather than listing details that are unnecessary.
"Black Rock glared at the train, remembering the events of the previous year. She had been attacked by ghosts and stranded on a snowy mountain, but at least she made some new friends. One that stuck out in her mind was a white haired Hanyou named Dante. Black Rock Shooter remembered how silly he acted and the highlight scene where he was fed a strawberry by a ghostly waitress. She also remembered how underneath all that silliness, he was a decent fighter. Getting back to reality, Black Rock saw the conductor at the door. He beckoned her to the train with his hand while wearing a warm smile. Black Rock Shooter narrowed her eyes, reluctant to board the train, but then sighed, relenting."
I'm not gonna lie this is very well done. Your flashback was short and didn't go on a tangent that might have bored me but still got to the point. Again still looking for what I can criticize and not finding it.
"The Other Self walked to the train and got onboard. Looking around, the feeling of the train returned to her. But it wasn't all ominous. One glance to the window seat in front of her, and she spotted that same Hanyou. Black Rock smiled a bit and walked over to sit next to him as she did before. Looking in front of her, she saw Night Terror, whom she also remembered from the previous year."
Other Self requires prior knowledge to the anime and shouldn't be used until you write what it means in some other post or story before hand. Even though everyone in this audience already knows, for general writing you can't assume your audience will.
""So the phantom train returns again? This was rather unexpected I must say...""
This dialouge helps some to show what the other self is, but perhaps you should mention that it is her who is talking and whether it physically is heard or just within her mind.
"Nodding at that statement, Black Rock replied to it telepathically.
"I certainly never expected to get on this train again. But at least there are familiar faces here, so we can team up if things go sour, which they will, I'm sure."
She would then lean back and look out of the window."
Good ending as it leaves anticipation, however it may not apply in this post, but you should always think about taking control of the story even if it's not yours and adding some plot, unless the person who started the topic had something in mind and you might interfere with that it's always good to provide some inspiration to make others eager to post to do something about it. Though for the intro it may not be necessary. Very impressive and not much I can really comment on to improve.