Perhaps nature is our best assurance of immortality - Eleanor Roosevelt
This quote may have been inspired by the numerous cases in which nature had been able to resurrect herself in one form or another after disasters of mega proportions.
However, it could also be inspired by Turritopsis nutricula, a tiny (4.5mm) jellyfish that is biologically immortal. This is slightly different from the "true" immortality that we know and desire.
Being biologically immortal means that the Turritopsis nutricula will not die from old age, it can still die from incidents like being infected with diseases and being eaten (which is more a blessing, since being awake while travelling through a digestive system is truly like going through hell).
The Turritopsis nutricula, also known as the immortal jellyfish, can go all "Benjamin button" and transform back to a younger self when they are injured, dying on starvation or when they are simply too weak to survive.
The process of this transformation is very much akin to science fiction. When the Turritopsis nutricula feels its life being threatened, it will sink to the bottom of the sea floor, and then, magic happens.
Firstly, the Turritopsis nutricula will reabsorb its tentacles and become a gelatinous blob.
In that state, the cells that made up the mature Turritopsis nutricula will transform into different types of cells needed to revert to its younger self in a process known as transdifferentiation - For example, sperm cells present can transform into muscle cells.
Over several days, the blob will form an outer shell and grow stolons, which resemble roots. These stolons continue to grow until they become a polyp.
Polyp is basically the method used by asexual species to reproduce by the method of budding. So that means while the Turritopsis nutricula may be immortal, it cannot go on an eternal sexual journey. Ultimately, the polyp will produce a younger version of the jellyfish, and the process will start anew.
However, there is a loophole in this seemingly perfect system. During the Turritopsis nutricula's growth from the polyp to sexual maturation stage, the transdifferentiation process canont be activated, thus during this period the Turritopsis nutricula is vunerable to diseases and pedators.
But this is still the closest living example that we have come to witnessing immortality first-hand.
And with so little ocean exploration done, the likelihood of finding a species capable of true immortality is reasonable.