No, I would not say that it's a defining quality of fictional villains. That would have to be power. After all, a powerless villain is useless for the story and the narrative. read more
Good villains need plausible motivations to do terrible things, so requiring that they do terrible things in order to achieve immortality is a good way to explain why they are willing to be villainous. read more
The quest for immortality is a common motivation for villains, most commonly occurring with old or aging villains; normally, it is the fear of death that drives their pursuit. read more