Wayta, Trainer Prodigy's last ability affects only triggered abilities whose trigger conditions refer specifically to damage being dealt, such as the ability granted by Mephidross Vampire or the last ability of Wrathful Raptors. It does not affect triggered abilities that would trigger because of the results of that damage. For example, if you control an Ajani's Pridemate ("Whenever you gain life, put a +1/+1 counter on Ajani's Pridemate") and you activate Wayta, Trainer Prodigy's second ability targeting a creature you control with lifelink and another creature you control, the triggered ability of Ajani's Pridemate will still trigger only once.