Instructions
Go to the Miasmic Swamp, which is unlocked at the end of Chapter 2.
Smash the Flame Core necropol by attacking it with the the Flame Core. Once it's destroyed, run past it onto the bridge. Jump off the other end and head east to the Pegasus Hunting Grounds.
Approach Pegasus when he flashes orange and hide behind rocks when he turns to face you. He is spinning in a constant circle, making it easy to time when he's looking at you. If you approach him when he's not flashing orange or if he see you, then you lose the mini-game and have to start over. When you approach him, press the sub-weapon steal button, which is by default the left shoulder button. This will initiate the sub-weapon steal mini-game.
Press the action button when the big circle and the little circle overlap. Do this repeatedly until Perseus unlocks the title "Horse Whisperer." The Pegasus will be tamed and you'll be able to ride him.