A superhero bio is no different from any character creation process. If you haven't any previous experience in character creation, however, I believe there are plenty old forum posts that cover the subject.
If you really want to make something like that, have a look at other people's character bios and see what kind of information goes in. While it's mostly done for drawn and roleplaying characters, I have seen it for story characters, too. In the latter case, be careful to provide just enough information to make people curious about your character, but don't tell every tiny little detail.
Unhappy childhood. Inculcated sense of injustice. Absurd pseudoscientific bestowal of powers. First instance of using them in the interests of justice. Costume design. Lesson that with great powers comes great responsibility.