The one and only biologically immortal species on earth is a kind of jellyfish known as immortal jellyfish. The scientific name of this jellyfish species is Turritopsis Dohrnni. These type of jellyfishes are found in Mediterranean sea.
What this jellyfish actually doing is they prevent ageing by reverse cycling their growth from adult to infant. Thus they stays immortal through this technique by tricking even the death. Turritopsis Dohrnni's back ageing has been proved in lab observations.
There is another species that seen on Carribean Islands and North America called as Turritopsis Nutricula which is often mistaken as Immortal jellyfish by several medias and websites. And the picture shown in these websites and medias are Turritopsis Rubra which is seen on New Zealand islands. Both these species Nutricula and Rubra has not been observed to find the life cycle reversal like Dohrnii does.
So the title for creature which never dies belongs to the Turritopsis Dohrnii ( the actual immortal jellyfish ).