Elfen Lied
Lucy is a diclonius. She is able to use her telekinetic powers to operate her “vectors,” long arm-like extensions capable of inflicting great damage. She violently massacres the staff at the research facility where she was imprisoned, only to be hit in her helmet by a sniper’s bullet and fall into the ocean. The wounded Lucy is found by Yuka and Kohta, who decide to take care of the confused girl who washes up on the nearby beach. Lucy develops a split personality from the head trauma, and forgets the damage she had inflicted at the facility. They aren’t going to let her go easily though.