After the Dominators' gene bomb hit Earth during the Invasion!, many humans found their metagenes triggered and gained superpowers. One of them was Joseph Martin, who suddenly found himself possessing superhuman strength, endurance, and the ability to shoot powerful energy blasts. Furthermore, he lost all his hair, giving him a skull-like appearance. After being beaten up by hoodlums, Martin suffered extensive brain damage and lost his grip of reality. Inspired by a TV serial about a superhero called 'the Atomic Skull' (whose looks were seemingly based on the original villain called Atomic Skull), Martin adopted a costume and roamed Metropolis as the new Atomic Skull. In his own confused mind, he sees himself as the hero, while Superman is a threat to humanity that needs to be terminated. Atomic Skull is not a super-villain per se, but has sometimes been manipulated by criminals.
Except for the likeness with the TV version, there is no connection between Martin and Atomic Skull I.