At least 2x average human strength and speed. (Despite being able to lob double decker buses.)
No weak spots to concussive, blunt, or sharp force trauma.
Chemo therapy causes your body to basically age to near-death before becoming any better. Treating yourself with it constantly could prove fatal. 
Judging by the title, POST-Post apocalyptic. I'm assuming that chemo would be scare, and I'm being generous with that amount, so the character would likely die a quick death.

Again, these are just concerns I'm voicing because I'm noticing a character who will be quantifiably superior to everyone else in every way.