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.
How about a dragon how cheerfully rules over a kingdom; his people all know him for what he is, and dragons are looked upon as wise and benevolent creatures. Dragonslayers from other kingdoms coming to free it from 'tyranny' are likely to get beaten to death by peasants with cast iron skillets.