New Master Quest is a harder second version of Ocarina of Time with rearranged dungeons. It first came out on a GameCube bonus disc, and Ocarina of Time 3D includes it as an unlockable mode with some extra twists of its own.
Unlocking Master Quest
Finish the normal game. After that, you can choose between the normal quest and Master Quest when you start the game. Master Quest has its own three save files, so your normal saves are safe.
What's Different
Redesigned dungeons: every dungeon has new puzzles, new enemy placement and new routes, so knowing the normal quest won't get you through. The overworld, story and items are the same.
NewA mirrored world: on 3DS, Master Quest flips the whole game left to right, overworld and dungeons alike, and Link becomes right-handed. Any guide written for the normal quest has its lefts and rights swapped.
NewDouble damage: enemies and bosses hit twice as hard, like the Hero Modes in later Zelda games.
No Visions: the Sheikah Stones' hint videos are not available.
Its own Boss Challenge, with even tougher rules. See the Boss Challenge page.
Tips
Collect the overworld Pieces of Heart early; they are in the same places as in the normal quest (just mirrored). Our Heart Pieces list works for both.
Get bottles as soon as you can and keep fairies in them. With double damage, a fairy is often the difference between finishing a boss and starting over.
All of the 3DS improvements apply, including the Iron Boots and Hover Boots on a button and the touch-screen menus.