If a creature was dealt damage but regenerated (which removes all damage from it), it will still be a legal target for the second mode of the triggered ability.

You choose which mode you're using as you put the ability on the stack, after the creature has entered the battlefield. Once you've chosen a mode, you can't change that mode even if the creature leaves the battlefield in response to that ability.

If a mode requires a target and there are no legal targets available, that mode can't be chosen. You must choose another mode if able.