Life is more than capable of evolving mechanisms to increase or decrease it's mutation rate. On Earth Eurkaryotic cells with large genomes have developed nuclei to reduce their mutation rate and bacteria are more of a mixed bag with some even deliberately uping their mutation rate above what would be cause by radiation, etc. So in the long run eukaryotic life would just have to waste more resources on mechanisms to resist the effects of the radiation.
That doesn't follow, at all. If we're talking about Earth-like life, then any such life would need protection from radiation to be able to live long enough to reproduce. If such protection wasn't provided by the planet's atmosphere, then life there wouldn't move out of the water. In any case, the mutation rate would need to be extremely low, as it is with Earth life.
