Easter Egg: Link's Grave
In Elfheim, walk to the top of the town where all the gravestones are. Click the one to the left and it will say, "Here lies Link." Some of you may be familiar with the name.
Unlockable: Art Gallery
You must finish the game once.
Unlockable: Item Minigame
After acquiring your ship, hold the X button down and tab the Circle button repeatedly (as in, over fifty times). Eventually, you will have hit the button enough times that a secret minigame will pop up. If you beat this puzzle-related minigame, you will be automatically rewarded with a random item, which can then be found in your inventory.
Unlockable: Bestiary & Music Player
To unlock the complete in-game Bestiary, as well as a Music Player which has every music track in the game, you must beat the game once through.