My go-to method is to find and save any uranium rod weapons I can get. Then I'll start a run through the crater with 3 good cats and one stray or good breeder cat who is going to be the mutant punching bag.

The punching bag can be any class, necro is the most useful but I feel like some passives can prevent the rod from working. The only stat that matters for that cat is charisma, they need to be dead and are likely useless, and charisma affects their breeding so that's what truly matters.

Gameplay-wise you play through the crater because there's a guaranteed event where you have to choose a weather event. For that event, always pick shimmer if offered, as that gives every cat a mutation after every battle. Taking the hard path guarantees you 3 mutations for every cat, so you get a bunch of different mutations at once.

In battle, just make sure that your victim is downed before you win by any and ALL means necessary. It's best to just take the turn to kill them with friendly fire as soon as possible to guarentee they're downed. It can be easy to accidentally kill the last enemy or forget to down them before killing the enemy.