The goal is to make everyone happy before leaving forever. If you've seen Groundhog Day, think of the last day where he makes everyone happy.
Complete all of the Bombers' Notebook sidequests. (I know this is technically impossible. You can't stop Sakon from stealing the bomb bag AND finish the whole Kafei/Anju quest. For this challenge I'll just not help the old lady and instead do the Kafei/Anju quest)
Complete all the pre/post-dungeon quests. This includes: saving Koume and the monkey; snoozing the baby Goron and winning the Goron race; retrieving all the Zora eggs and bringing Lulu's voice back; and healing Pamela's father and defeating the king of Ikana Castle (the tedious Gibdo quest under the well is unnecessary)
Defeating the dungeon bosses again—the quick and easy way, no need to re-traverse the dungeons.
I just think it's a fun challenge