The
most radiation resistant organism in the world is
Deinococcus radiodurans according to this article and a load of others.
it does not specify the kind of radiation that it is resistent to but I strongly suspect it is going to be gamma and not neutrons.
The articles say that when the bacteria is subjected to a burst of radiation, its DNA is completely shredded but its repair mechanisms are such that it is able to put it all back together in a day.
However if this bacteria were subjected to a constant radiation source such as a reactor outer core (outer core has no fast neutrons left) where all there will be are a bunch of gamma rays, it would not have time to repair the damage and would still die.
I just don't buy it that these things could survive in a reactor.
These things have been known to survive the level of irradiation (gamma) used to sterilize food but that is still only an infinitesimal amount of the gammas in a reactor core.
The bacteria can survive 1.5 million rads of gamma or X-ray radiation.
An average reactor pressure vessel receives a gamma dose of 10,000,000,000,000 rads. (see
this paper on reactor design)
That is just gamma. On top of that the fast and slow neutron reactons would physically convert almost every Carbon atom in the whole organism to Beryllium within a couple of hours.
No amount of DNA repair is going to save them when there are no available Carbon atoms.