Little Wing
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

My, my! Hatchlings are very popular this season! I will tell you what I can about them. When they grow larger they are called striders and may be ridden. Later they mature into flying creatures called wyverns.
Take a look at this Katz. It's so cute and cuddly it's hard to imagine that they become such huge creatures! Ha Ha...
What is your interest in hatchlings? Would you like to raise one?
Previous owners of hatchlings have sought advice from Elder Cronos in Hunters Village.
Quest steps

Quest that must be completed in order to obtain a pet hatchling. Visit Pet Manager Cooper and tell him that you wish to raise a hatchling. He will tell you to seek help from Elder Cronos of Hunters Village.

After collecting the items requested by Elder Cronos, find Maria in the Town of Dion and ask her to make a Fairy Stone for you. Take the Fairy Stone to Cronos and he'll tell you what you need to do next.

Take the completed Elven stone to Guard Byron and ask him about fairies.
Go to Fairy Valley and find a fairy who will talk with you.

Take the juice of monkshood that Fairy Mimyu gave you to the drake or wyrm that she introduced you to.
Recover 20 stolen eggs.

Take the eggs to Fairy Mimyu.
This quest has no goals mapped: it is a guide task, there are no mobs in it.