Pursue the condor as it flies around various locations of Tiny-Huge Island, including the starting area, mountain, tree area, and beach. Use Yoshi's speed to catch up to it. When you get close enough, dive from Yoshi's back with a ground pound to stun Klepto The Condor and recover your red Mario hat.
After retrieving your cap, jump on Klepto The Condor's back and stay there. This will prevent it from flying away again and allow you to reach the large, hidden area on top of the mountain. Here, you'll find the fourth star. Simply grab the star to complete the mission and add this star to your collection.