Kakugo no Susume (1996)

Apocalypse Zero

A series of natural disasters has reduced the world to rubble, with the survivors doing whatever they must to survive in a world gone mad. But one young boy, Kakugo, gifted with amazing martial arts and a superpowerful suit of armor by his late father, has been charged with making the world (or at least his school) a safer place. But his sister has a matching set of skills and equipment, and she`s on a mission to bring peace to the world... by wiping out humanity! (Source: AnimeNfo)