The character was forced to undergo a radical treatment to save their life. This might be a cancer-curing trammaton radiation treatment with unexpected results, or a full synaptic download into a lab animal or fully prosthetic body.
Example: The Hulk (Marvel Comics)
The character was altered purposefully at a very young age, or possibly in utero. In an effort to eliminate human “weaknesses,” the character may have been soaked in the Achilles formula, had their genes resequenced, or had their subatomic structure blended with that of a komodo dragon.
Example: Dr. Julian Bashir (Star Trek: Deep Space Nine)
The character was suddenly exposed to something that has granted them powers, be it cosmic radiation, toxic chemicals, bitten by a genetically altered shrew, or struck by lightning. The character has been forced to abandon their old life, and seeks to build a new one for themselves.
Example: The Fantastic Four (Marvel Comics).