Villains who cannot die and can live forever; this condition is referred to as "complete immortality" as opposed to "biological immortality" which simply means they have an infinite lifespan but can die from physical or mental trauma.

Such villains will survive from nearly anything thrown at them (e.g. nearly every Olympians Gods from God War), or at least resurrect/regenerate after being destroyed (Chucky). For obvious reasons, these villains are amongst the most difficult to beat.

In many fictional universes, they can still be defeated especially if they owe their immortality to special magical items that, if destroyed or stolen, will simply kill them or leave them vulnerable to death, such as Davy Jones' Heart, Lord Voldemort's Horcruxes, or Kel'Thuzad's Phylactery. Other characters like Sigma can return as long as his cognitive circuits are not completely destroyed. Also, other divine entities have such powers to kill them.

Also, please note that ageless villains with "biological immortality" do not count.