You know that whatever the species, it had to breathe and develop limbs for walking. It's seems incredulous that a fish could do that. If you are conditioned into believing such an incredible tale, then I suppose you could believe anything. I put it in the too hard basket simply because I have no evidence that this event took place.
I used the term fish/animal to dumb it down enough so you might understand it. "Fish" and "animal" are not biological terms. The animal was something like Tiktaalik but would not readily fit into a modern categorisation.
So...something which looked biologically like a fish wandered into shallow water at the edge of the sea. Since there was no other creature there to complete it had free access to all the vegetation and little sea critters it could eat - fantastic. Over time fish/critters which could get closer to the shore had more access to food and (as a result) more kids. It turned out the fish/critters with stronger fins could lever themselves into shallow water = more food.
While the fish critters were slowly climbing out of the water a small change to gill structure allowed some of them to absorb oxygen directly from the air. No big deal - oxygen absorption from air is not that different to oxygen absorption from water - some animals (like pigs and rats and probably humans) can actually breathe through their anus. I'm currently trying to learn how to do this but with mixed results.
So with stubby little fin/legs, the latest generation could lever itself up and breathe out of water. They now had access to all the onshore edible goodies, no competition and no predators who could reach them.
The rest is evolutionary history.
What is this, Ripley's believe it or not. I want the name of the species involved, not speculative guesses. Either you know or you don't know.
In modern terms think of mud skippers. The actual beast was an early form of Tiktaalik.
It is a giant leap to progress from a fish into say a lizard, then an even bigger leap from a lizard into a mammal.
Not really. The big difference between a lizard and a fish is probably a bit more neck mobility. In fact there ain't much difference between a fish and a human if you think about it. Bi-lateral symmetry, similar set of internal organs, keratin coating (skin, scales, feathers, hair, fur - same stuff), eyes, a digestive system, oxygen breathing. Given a bit of thermal regulation, enough time and a bit of modification to the reproductive system

and your basic fish critter shifts from fish to lizard to mammal to primate fairly easily.
So...that's Evolution 101 according to OB.
OB