What are the major evolutionary trends that developed among major vertebrate groups, specifically those that allowed for the transition from aquatic to terrestrial life?

One of the greatest developments that allowed for life on land was the development of limbs. Limbs allowed for greater movement on land. These limbed animals were called tetrapods. They started to appear in the late Devonian era over 330 million years ago. While the first limbs ended in webbed appendages, later feet were not webbed, and some had claws which allowed for digging. In time, the feet of vertebrates adapted for grasping prey.
Another important development was the development of lungs. In their early stages of life, amphibians are equipped with gills, but they later transition to lungs when they achieve adulthood. While the first terrestrial vertebrates of the Devonian era had both lungs and gills, the terrestrial vertebrates would transition to lungs and soon lose their dependence on water for reproduction or oxygen, though water would still be important for hydration.
There are many reasons the first terrestrial vertebrates evolved. The most common theories include predators and competition, though some scientists speculate that extreme drought may have been a factor in driving the first vertebrates to land.
https://ucmp.berkeley.edu/vertebrates/vertfr.html