Gunnm (1993)

This movie takes place in a distant future, and is the story of a the young cyborg Gally, who is found on a scrapheap by the Cyberdoctor Daisuke Ido, who rebilds her and becomes her surrogate father. Gally has no memory of her past, but soon displays remarkable fighting skills. She starts working as a bounty hunter and meets a young boy Yugo, who has the impossible dream of going to Zalem. A giant satelite floating above the city. Not realising that Yugo's dream can only end in missery Gally sets out to help him.