There is a species of jellyfish that is immortal

I'm not sure of the exact definition of immortality, but I wouldn't really count this.

Without diving too far into philosophy of self: if I right now I turned into a newborn child (with my DNA and made from my current mass), I would be dead. Sure there would be some kid who was pretty much a clone of my younger self, but anything and everything I would consider part of me (my mind, my memories) would be gone.

It's still really impressive, but without preservation of the mind I think it falls a bit short of what most people expect when they hear "immortal".

"The turriptosis nutricula's cell development method of transdifferentiation has inspired scientists to find a way to make stem cells use this process for renewing damaged or dead tissue in humans."

One word: Zombies

There is a species of jellyfish that are immortal.

Yes, but only potentially. The wikipedia article highlights that none have been sufficiently examined to be that old because of the lack of adequate dating systems and the propensity to "predation or disease" in the plankton stage.