Back home, do some stocking up and/or upgrading at Beedle’s shop and the Bazaar. Do other desired sidequests, as well.
Once you’re ready to continue, go to the second floor of the Knight Academy and speak with Headmaster Gaepora in his room about the Triforce. It seems that he won’t be much help with this matter.
As you try to leave the room, he does suggest that Owlan may know something about Levias within the Thunderhead. Go speak with Owlan, next door. You then will learn that Levias has recently become possessed by some kind of monster.
Owlan will agree to instruct you on a new charge, the Spiral Charge, for your Loftwing for use in the upcoming battle with Levias. All you have to do is a normal charge.
You are then to hit 10 of the targets in the sky within two minutes (one per 12 seconds on average). No real strategy here - practice makes perfect, which is the whole point of this required exercise.
Afterwards, you are told to go to the Lumpy Pumpkin because its owner makes a yearly offering (of pumpkin soup) to Levias. Use a platform and start flying.
Head southeast to the Lumpy Pumpkin. If you’ve never been there, it is the island with a massive pumpkin on it functioning as the main and only building.
The Lumpy Pumpkin
Upon arriving, go into the Lumpy Pumpkin. Go to the counter and speak with the owner/cook behind it. He’ll speak of his usually-annual offering of soup to Levias. He cooks up a batch of soup for you to take, which Scrapper then comes to carry around.
Save at the Bird Statue outside, then fly northwest into the Thunderhead.
Inside the Thunderhead
Upon arriving, descend and tilt more northward towards the rainbowed island - you can’t miss it. Also watch it - the birds in the area will try to attack in earnest.
Once you reach the island, dive onto it to quickly meet Levias, who is very obviously possessed by some beast. And so, you are to battle him.