A player loses life if they pay life.

You put only one +1/+1 counter on Vengeful Warchief, no matter how much life you lost.

If you pay life to cast a spell or activate an ability, you don’t put a +1/+1 counter on Vengeful Warchief until after you’ve finished casting that spell or activating that ability. You put the counter on Vengeful Warchief before that spell or ability resolves.

If Vengeful Warchief comes under your control after you’ve already lost life in a turn, its ability can’t trigger during that turn.