There are many ways in which animals can be rendered “invisible”:
Live Someplace Dark: Obvious, but effective. Live in a cave, or deep underwater, or be nocturnal.
Camouflage: American Bittern, octopuses, leopards, deer, nighthawks… the list goes on forever.
Cloud the Minds of Men: Only known to The Shadow, and maybe the thylacine.
Hide: Another simple but effective form of invisibility, if you go out in broad daylight.
Make Light Pass Around You: Only known to one species of predator.
Make Light Pass Through You: Transparency is a quality often utilized by aquatic animals, but rarely by terrestrial animals. My favorite: the Glass Frogs of the Central & South American rainforests.
Live Beyond the Visible Spectrum of Light: And here’s where I arbitrarily choose my “Invisible” Animal:
It’s a Red Shrimp, so called because, uh. It may be glaringly obvious to us, but consider this: the “red” part of the light spectrum can only penetrate about 10 feet into the ocean’s depths. That’s why, if you cut yourself while diving, your blood appears green, or black. So as long as it doesn’t come to the surface, a red animal like this shrimp is effectively invisible.
Only problem is, there’s something down there that can see it.
It’s a Stoplight Loosejaw. The jaws are partially detached from the body for a further-reaching bite; when you live in the darkest depths of the ocean, you can’t afford to miss food when you bump into it. Then there are those two bioluminescent patches near its eyes. The “green” light (closer to “blue,” really) is an all-purpose headlight; blue light reaches further underwater than any other slice of the spectrum. But the “red” light is for catching red animals. It’s night-vision crossed with secret decoder glasses; by shining red light on a red shrimp, the invisible becomes visible. And because most sea creatures never evolved the ability to see “red” — because, why bother? — the red shrimp will never see the glowing predator coming. Think of the night-vision scene with Buffalo Bill and Jodie Foster in “Silence of the Lambs.”
My point — as I always have a point — is that Nature creates superpowers, and Nature will find a way to nullify them. Invisibility is useful, but you can still be found out by sound, or smell, or body heat, or the tiny bioelectric impulses your beating heart discharges into the water. Superpowers necessarily create supervillains.