Immortals are villains who cannot die and can live forever. This condition is referred to as complete immortality as opposed to biologically immortal which simply means they have an infinite lifespan but can die from severe trauma.

Such villains will survive nearly anything thrown at them or at least resurrect and/or regenerate after being destroyed (e.g. nearly every God of Olympus, Chucky, William Afton, etc.). For obvious reasons these villains are among the most difficult to beat.

In many fictional universes they can still be defeated, especially if they owe their immortality to special items that if destroyed or stolen will kill or leave them vulnerable such as Sauron's One Ring, Davy Jones' heart, Lord Voldemort's Horcruxes or Kel'Thuzad's Phylactery. For example, Sigma can return as long as his cognitive circuits are not completely destroyed. Other Cosmic Entities or Deities may have such powers with which to kill them.

Also, please note that ageless villains and those who are biologically immortal do not necessarily count. If the villains eventually indeed die it is often in disgrace, especially if they had to kill others and/or sell their soul in an exchange.