Pegasus has a lot of health, like any final boss, and does not really damage the player at all until after a damage phase. You just have to put enough damage into Pegasus to knock him out of the sky and then use your Special Weapon to deal massive amounts of damage to him while he is glowing orange, and repeat that until he is defeated.

If you want more information on how to prepare and defeat this boss fight, you can view our detailed guide for Ancient Evil's main quest, Greek Tragedy.