A boss is the climax of a dungeon or temple. It's what you work towards, solving puzzles, fighting enemies, and avoiding traps, to be thrown into combat against a being more powerful than your character could ever imagine to be at that point in the game. Henceforth, the boss MUST BE the most memorable part of a dungeon, in my opinion.
From there, a boss fight, especially in a 3D Zelda title, is expected to be big, strong, and epic. There aren't many bosses in Zelda titles since Ocarina that aren't bigger than Link. I'm struggling to think of just one at the moment. Examples of my favorite boss battles that possess this epic sense of a titanic struggle include Twinmold from Majora's Mask, Bongo-Bongo from Ocarina, and the Helmaroc King from Wind Waker.
Every boss fight should also integrate the item in the dungeon in some way, shape, or form. Think about it. You are entering a dungeon that that boss is lord of. It hides its one weakness inside the dungeon, guarded by its strongest minions (mini-bosses.) You make it all the way to the boss and you have in your possession the one item the boss fears. From the slingshot to the Megaton Hammer, the items gained in dungeons are there because they are the bosses weakness, thus highlighting their importance.
Bosses should always increase in difficulty as your progress through the game. This makes sense because as you progress further into any game, you collect better items and learn how to control your character better and more fluidly. To give you bosses of similar difficulty throughout the game is about as useful as repeating the same fight over and over. An easy way to explain the difficulty of a boss is the puzzle-solving aspect of a boss fight. Every boss has a weak point that you must find. Using Ocarina as an example, Gohma's weak point is her eye, which is easy to see. King Dodongo's weak point is his gaping mouth. A little bit harder to see but still rather easily accessible. Starting with Barinade, the bosses weak points become harder and harder to access. Barinade's is its underbelly, Phantom Ganons is his shock ball attack. Volvagias is its head, Morphas is its core/heart, Bongo-Bongos is its eye, and Twinrovas are their opposite powers. Now, you may stop and say, "Hey, wait! Isn't it obvious that Morphas weakness is its core/heart? And that Bongo-Bongos is its giant single eye?" The fact of the matter is, it isn't just about finding the weakness but also finding out how to exploit it. And that ups the challenge of bosses even more.
So, to review, a boss must have/be:
-Memorable
-Epic, grand, large.
-Make use of the dungeons item
-As difficult as should be expected at the point of the game you're on.