Elfen Lied

Elfen Lied takes place in basically the current day and age of Kamakura, Japan with a twist. The story centers around a girl with long pink hair named Lucy aka Nyuu. It all starts out with her imprisoned on an unidentified island where she is bound and her face is covered with a metallic mask. She is nude the rest of the way and once she escapes and her captors feel her wrath, she is still continually nude. Basically, the series is quite gory, as the main character Lucy uses an invisible set of hands (called Vectors) which rip apart her enemies without her ever having to raise an actual physical finger.

Lucy ends up escaping the island, leaving a trail of mutilated victims in her wake. She jumps off a cliff and into the sea just as she's shot at. Eventually, she's swept up on the shore of a beach where a young boy named Kohta and his cousin Yuka find her.

This is where Lucy's split personality of sorts comes in, when she's named Nyuu instead of Lucy. Nyuu is an innocent version of herself, another part of her personality that when it comes to surface, all that she can say is "Nyuu!" Lucy herself, on the other hand, is the more dangerous part of her persona. Lucy, as you can imagine, is not human but is instead a new strand of human being called a Diclonius. Diclonius were created by human experimentation and upon creation they have some visible differences, the most notable being little horned protrusions from their heads and of course the translucent group of arms that branch off of them in order to tear up their enemies in times of confrontation.

It's eventually revealed that Kohta had known Lucy in their youth but that it hadn't been apparent at first. Lucy was terrorized as a child and as a result has developed a great dislike of the human race. Of course, this does not include Kohta. Other Diclonius begin to arise in order to take out Lucy and that's when a great many battle starts in order to fight for Lucy's freedom and her new friend's safety.