To get the kill counted on your bestiary, you got to get at least 1 hitpoint damage. Just one! Easy like that. That's why most people just use firebombs or gfbs to burst all the cave when it's full on a rapid respawn weekend.
But, for loot or quest purposes there is a different criteria. Each boss/monster has a minimum contribution you have to give to get the right of the loot or to complete the quest mission. Of course that's not a known formula, but I think it doesn't need to be just damage dealt, but may include healing of blockers or even damage taken (blocker duty) and such.
Hope have helped!