Start by heading to Glastheim (P) and walk to the western part of the map. Keep walking until you find Coco (located around 47, 163). In order to talk to him, you must have a Ring of the Ancient Wise King equipped.
After talking to Coco, it will send you to find a man by the name of Noetal in the Library. Head to the northern part of the map to the library and enter it.
Walk down the stairs, to the back of the library and speak to Noetal (Located around 163, 122).
After speaking with him and agreeing to help, he'll tell you to fetch some items (Listed below). Go off and collect those items for him, then return.
After he takes the items, he'll give you the cure (It will be displayed in your chat box, not an item).
Return to Coco and he'll tell you to give it to his master. Walk a bit to the right and you'll see a girl sitting (Located at 63, 164).
Speak to her and after she drinks the cure, she will get better and reward you with a Teardrop. This marks the completion of this quest.