Little Wing's Big Adventure
What to kill and where to find the goals.
Repeatable: the items to hand in drop from the targets without limits, and you can run it again and again. Go kill those mobs and the quest comes along for free.
This is an exchange chain: the reward is collected as items traded at an NPC — the shop's full stock is not laid out here.
Story

We've had this conversation before, haven't we? As I said, raising a hatchling requires resolve, which you haven't yet proven. Have you learned your lesson yet? Are you ready to have your hatchling transformed into a strider?
Whether I know how to do it or not is no concern of yours...
The thing about hatchlings is... Wait! What is this? When did you switch the dragon flute? Oh, come on! How long can you go on acting like this?
Quest steps

Elder Cronos suggests you consult Fairy Mimyu concerning the raising of Hatchling to Strider.

Fairy Mimyu examines your hatchling and tells you the story of the four fairy trees and their guardians. She tells you to feed the sap of these trees to your hatchling. Go to each of the four fairy trees of wind, star, twilight and abyss and let your hatchling drink their sap. You must guard your hatchling as it drinks. When it has finished drinking, attach a fairy leaf to the fairy tree.
Collect: Fairy Leaf × 4

Your hatchling has drunk the sap of all four fairy trees-- the wind, star, twilight and abyss. The preparations for its growth have been completed. Return to Fairy Mimyu.
This quest has no goals mapped: it is a guide task, there are no mobs in it.