In order to get this achievement you'll need to open the Indigo Quarry, as this is the only place where rad slimes will spawn. once you've found one, simply stay in its radiation bubble for 15 seconds. I let the radiation gauge fill to 95 before i left it. Be sure you don't stay in more than one radiation field at a time, as that makes the gauge fill much faster.
Here's my video for every achievement if you'd prefer. Skip to 2:14 for That Only Works in Comic Books.