It actually seems to be based on the boosted stat from rare pets that you can catch. Most of the rares have boosted Speed or Attack, but occasionally, you'll encounter pets with absurd health stats. Last night, while farming a rare Twilight Fiendling, I encountered a rare Cockroach, lvl 22, with ove...

I'm actively scouring the pets I've looked up recently to find it, but I know I saw an ability just like that. To be honest, though, you're probably better off downloading the Pet Battle Teams addon and making several different teams at varying level tiers. For instance, now that I've completed all ...