Vengeful

Vengeful villains or Seekers of Vengeance are villains who commit their crimes under the premise of vengeance (also called retribution or revenge), whether it be for a wrong committed against them or their people/race, something done to hurt their friends/families, a heroic action that caused them great loss, a personal reason, etc.

They are similar to a nemesis, but with a few slight differences. First of all, a seeker of vengeance is a specific type of nemesis, being concerned only with revenge, while a nemesis encompasses all types of motivations.

Also, a nemesis is an enemy who is created through the hero's own actions, but a seeker of vengeance might already be an enemy to the hero and is seeking revenge for a perceived wrong dealt to them by the hero (i.e. Opal Koboi from Artemis Fowl). Seekers of Vengeance may also be pursuing revenge against neutral characters or even other villains in Evil Vs. Evil scenarios (for example, Ransik or Jean Descole).