All biological creatures die. Even if one survives predators, diseases, malnutrition, and accident, it is inevitable that one would die due to senescence. Senescence, or biological aging, is the change in the biology of an organism as it ages after its maturity (Wikipedia). In other words, it is simply dying from old age. However, there are at least two beings that may not be susceptible to senescence: (a) the Turritopsis nutricula (immortal jellyfish), and (b) the simple fresh-water genus hydra.

As such, these creatures are deemed biologically immortal!