One adjective to describe "having fast regeneration"

As far as I know, there is no single word that describes this specifically.

You could say that an animal is resilient:

[Merriam-Webster]

: characterized or marked by resilience: such as
a : capable of withstanding shock without permanent deformation or rupture
b : tending to recover from or adjust easily to misfortune or change

But that's more of a general term, and both fast and regeneration are only implied. Also, it's likely you'd want to use an adjective like highly in front of it anyway.

Some animals are able to regenerate in dramatic fashion, as with salamanders who can regrow lost limbs. Humans can regrow parts of their liver, and some children can even regrow a lost fingertip.

Still, there is a difference between how extensively something can regenerate and how quickly it can regenerate.

The Forbes article "Deadpool's Healing Factor Is A Realistic Superpower" says this:

Some species have unlimited regenerative potential. Most impressive are salamanders, the group of amphibians that includes newts and axolotls. Following amputation of a leg, salamanders can regrow a whole limb from the stump. They can also replace vital organs such as the heart or brain.

Why don't more animals regenerate? Although it's useful, regeneration isn't the best survival strategy because healing wounds is a trade-off between speed and accuracy. Perfect repairs can take time, whereas immediately closing an open wound minimizes the risk of infection or bleeding to death, although it does leave scar tissue.

But the ability to regenerate isn't pervasive enough that we've needed to coin single words for either extensive or fast regenerative abilities.

Lacking such, you will have to resort to the normal adjectives in front of the word.