Classified as a category 4 threat, the Elib is somewhere between a vampire lord and Godzilla for limits of escalation. Yes, I would consider using a nuclear device to kill just one. I am that sure that I want it dead.
"It is said that among those people they have a loathsome custom- that they keep a spotted dog always waiting beside the gate of the yard where they bury the dead, and that in every funeral they allow this spotted dog to feast upon the dead, so that it grows fat and wise with the knowledge of the dead... Many necromancers do seek out these spotted dogs, and ask of them sciomantic knowledge, or take them as familiars." -Author unknown, "The Ways of the Necromancers"