At least part of that protection is conferred by the DNA-binding protein Dsup [1]. So minimally the cost is 1) producing the (unique, as far as we have searched) protein, and 2) dealing with DNA which has Dsup bound to it.
There is no free lunch, but it's actually a pretty interesting protein that seems to somehow sacrificially prevent double-stranded breaks of DNA by ionized radiation. It's likely not much more than a metabolic cost - though there is some possibility that it affects some gene regulation. When Dsup was put into mammalian cells it did confer to them protection from radiation damage.
There's a feature budget only in that there's a cost/benefit restriction for every living thing. Usually the big cost is how many calories does this gene cost vs how much does this gene benefits the organism (or it's close relatives).
What's interesting about having high radiation resistance, is that I could see a cure or vaccine for cancer could be introducing (or possibly expressing) genes that cause our cells to spend a lot more calories to repair its DNA than they already do. And the skeptic in me thinks it'll probably be marketed as a diet pill :)
Or more likely you don't see those kinds of creatures because there has been no reason for evolution to select for all those abilities in one species. It's good enough to have one of them.
But that says nothing as to whether genetic engineering could produce such creatures.
There's a "feature budget" in any organism, and it's the main reason why you can't have creatures that could fly, and run fast, and live underwater.