1. Speak with Dodoh on Fun Fun Island
This sidequest cannot be started until you have found Kukiel and met Batreaux.
You must also have repaired the Ancient Robot, Scrapper.
Visit Fun Fun Island after repairing the Scrapper to find Dodoh depressed because his Fun Fun Wheel has fallen beneath the clouds.
If you agree to help find the Fun Fun Wheel, Fi will set the wheel as a dowsing target and suggest that it has fallen into the Lanayru Desert.
2. Find the Fun Fun Wheel
Drop down to Lanayru Desert at the Bird Statue on the southern end of the largest region of the desert (the actual desert; not the mines).
You’ll find a mine cart and two piles of rocks nearby. Ignore the mine cart and use bombs to blow up the rocks to reveal a Timeshift Stone.
When you activate the Timeshift Stone, vines will grow on the nearby cliffs on the eastern side of the area. Climb the vines and follow the path at the top of them to find the Fun Fun Wheel.
Ask Fi to call Scrapper to take the Fun Fun Wheel back to the skies.
3. Deliver the Fun Fun Wheel
Return to the skies and fly to Fun Fun Island. Scrapper will drop the Fun Fun Wheel and you will receive five Gratitude Crystals from Dodoh.
Fun Fun Island Mini-game
Completing this side quest unlocks a mini-game on Fun Fun island where you can win (or lose) Rupees. Dodoh will fire you out of a cannon and you must fall through various rings and land on a spinning wheel at the bottom.
If you do well, you can earn a lot of Rupees. If you fall on the wrong spaces, you can also lose Rupees.