He survived, grew up to be a strong young man, and as is so often the case with young men, got into foolish dares. After being goaded by his prospective step-father, Perseus ventured into the wilderness to kill the Medusa, a horrible snake woman who could turn people into stone with her gaze. Along the way he met up with some of his siblings (also gods, remember) who gave him a set of winged sandals and a mirrored shield and a pretty nice bag. He then found the Medusa, slew the Medusa, and tossed her head in the aforementioned bag.
That's an interesting adventure, but what really makes him superheroey are the adventures that came next as he wandered around, righting wrongs. Also of note: He apparently lugged Medusa's head around for years, like it was his mascot or something. On at least three separate occasions, he dragged it out of its sack to win an argument by turning someone into stone.
They don't allow this move in debate club anymore.