Battle Angel Alita 

In a dump in the lawless settlement of Scrapyard, far beneath the mysterious space city of Zalem, disgraced cyber-doctor Daisuke Ido makes a strange find: the detached head of a cyborg woman who has lost all her memories. He names her Gally and equips her with a powerful new body, the Berserker. While Gally remembers no details of her former life, a moment of desperation reawakens in her nerves the legendary school of martial arts known as Panzer Kunst. In a place where there is no justice but what people make for themselves, Gally decides to become a hunter-killer, tracking down and taking out those who prey on the weak. But can she hold onto her humanity as she begins to revel in her own bloodlust? (Source: Kodansha USA, edited)