Allow me to introduce to you the epaulette shark:
This one species stands out over the other 511 in that it can breathe out of water. How? It actually has several adaptations:
- They slow down their circulatory and respiratory rates, thus reducing the demand for oxygen.
- They power down their brains for that same purpose.
- Their fins are modified into something akin to legs, so the shark "walks" rather than swims.
However, there is a problem--this survival strategy has a maximum limit of just one hour.
In an alternate Earth, the Paleocene-Eocene Thermal Maximum still happened 56 million years ago, except that it lasted much longer (say, three to four times longer.) Some waters got so hot and so acidic that some shark species escaped extinction by crawling out onto land, occupying the niches of such bony fish as mudskippers and walking catfish. These "lungsharks" can stay out of water for a maximum of four days.
But air-breathing bony fish have the one thing that makes this possible for them but not for sharks--a swim bladder. Since it's already filled with air, it's easy for some species of fish to modify them into something comparable to a lung. But sharks don't have swim bladders, so they have to find some other method to make air-breathing possible.
Within the constraints of 56 million years of evolution and with no swim bladders, how would lungsharks be able to breathe air within a four-day limit?