Find and obtain the Jewel of Wind.
If you have already reached level ten on your green experience bar, you should obtain it directly. If you haven't, the message "Not enough Experience!" will appear.
In order to clear the event and obtain the Jewel, you will need to raise your green experience by leaping on the winged pigs in the Lava Caves or the spiders in the Watch Tower. When you have reached level ten, go back to Phoenix's nest and obtain the jewel to clear the event.