Throw in a pinch of Deinococcus radiodurans
Deinococcus radiodurans can live through blasts of radiation thousands of times greater than the level needed to kill a Human. A dose of 500 to 1,000 rads is enough to kill a person, but D. radiodurans has thrived even after being exposed to 1,500,000 rads. I don't think that all of its defenses could be incorporated into eukaryotic cells, but some of them probably could.