Mardock (2003)

Blurb:
'Why me?" It was to be the last thought young prostitute Balot, would ever have... as a human, anyway. Taken in by a devious gambler named Shell, she became a slave to his cruel desires and would have been killed by his hand if not for a private investigator and his self-aware Universal Tool, Oefcoque.

Now a cyborg, Balot is not only nigh-invulnerable but has the ability to disrupt electrical systems of all sorts. But even these powers may not be enough for Balot to deal with Shell, who offloads his memories to remain above the law, the immense assassin Dimsdale-Boiled, or the neon-noir streets of Mardock City itself.

Source: www.anisearch.com/manga/8919