You actually need: The Shield, The bunch of Bananas. The Shield is 30.000 yen, the Bananas 10.000. You can get both pretty early in the game if you go to the bigger park near the middle area.

How to fly - You should get a lot of "bombs" first since you will need a lot if you really wanna do it right. Best, get a higher place where you can actually test it. Equip the shield and activade it, Equip the bunch of bananas, Throw the bunch of bananas "near" to you. At the highest point of the arc, let the bananas go. You will get a push upward. Doing it in the right time you actually are able to fly away to secrets and like.