Question

Which vertebrate class is considered to be the first that was entirely terrestrial?

Answer 1

Reptilia.
Reptiles were the first animals to develop shelled eggs, meaning they could be laid on land rather than in water as is necessary for the shell-less eggs of amphibians and fish. They also developed dry, scaly skin to prevent the moisture loss amphibians experience through their moist, permeable skins when on land.

Answer 2

The first entirely terrestrial vertebrate class totally independent from the aquatic habitat is the class reptilia.