I tend to only see this in that volcano.
There will always be one motherfu**er in each of those rooms of the volcano hogging all 3 or 4 Lizardons. I'll come back an hour later and I still see them in there. For what? A spot on the leaderboard? Grind to 1M baddy kills?
In order to ensure the baddy is yours if you're fighting for one with another player, you need to take over 50% of their HP. i.e you need to hit a rebel for 2.0 of 3.0 HP (4 hits). Basically, you just need to hit the baddy more times than someone else, even if someone else kills the baddy.