In traditional Zelda fashion, all your puzzle-solving and enemy-slaying in each of the special dungeons culminate in an exciting fight against its unique boss. You'll have to make use of the new weapon you got in the dungeon to defeat the bosses, excluding the last two. These are the bosses you'll find in each of the Temples in The Legend of Zelda: Twilight Princess.

Diababa
Diababa is the dungeon boss from the Forest Temple. The fight is separated into two parts:

Part I
The boss battle begins with two plant tentacles attacking you - stand near the back wall to avoid their attack. On either side of them are spider-bombs. Lock onto one of them with your boomerang, then lock onto one of the tentacles and throw your weapon. It will pick up the bomb and then proceed to the tentacle destroying it in the process. Repeat this for the 2nd one as well. Note - using the Gale Boomerang, it is possible to move multiple bombs at once!

Part II
After both tentacles are destroyed, the boss's true form will be revealed. Throw your boomerang towards him to trigger a short cut-scene. It turns out the baboon you defeated a short while ago wants to help you! He will swing back and forth carrying a bomb between his feet. Use your boomerang to lock onto the baboon first, then the main part of the boss, and let it fly. Like with the tentacles, it will carry the bomb towards the boss where it will explode. Afterwards, the boss's head will fall limp to the ground - slash with your sword at the eye sticking out.

When he retreats, he will fire a poisonous liquid at you. Stand back against the rear wall to evade it. Afterward, repeat the above process to defeat him.

Fyrus
Fyrus, the dungeon boss of Goron Mines, appears to be quite intimidating, but with the right technique, he's a pushover. Keep your distance and fire an arrow into the pink spot on his forehead to stun him.

While he's stumbling around, grab one of the chains trailing behind him and equip the Iron Boots to trip up the boss. Once he's down, run up and slash the pink spot on his forehead with your sword.
If the boss gets uncomfortably close, you can roll between his legs to escape quickly. Furthermore, if he launches his wall of fire attack, seek cover behind a pillar for protection.

Morpheel
Morpheel is the overlord of the Lakebed Temple. He may seem daunting, but thankfully his lack of attacks make him a push over. He has two forms with his eye as the weak point both times. Lock onto the floating eyeball amongst the tentacles and use your Clawshot to pull it towards you. Just watch out for the bomb fish swimming around during this segment. Also, if a tentacle reaches next to you, hit it with your sword to knock it away, or else it may grab you. When the eyeball is close, slash it with your sword a few times to make the boss fully reveal himself.

Although he's quite a fast swimmer, Link can catch up to him by cutting through the center of the arena, or approaching him from head-on. Just stay away from its mouth as it can pull you in to deal damage. There's an eyeball on its back that you'll have to lock on to, and then Clawshot to pull yourself over to it. Once Link gets situated, lash with your sword to deal damage (sorry, spin-attacks won't work here).

Stallord
In the Arbiter's Grounds, you'll find this fossilized creature-thing called Stallord.
Stallord will appear once you near the skull in the center.

Use the spinner on the railing and ride around to the boss's backside (make sure to jump off if am enemy spinner nears on the railing). Head towards the boss's backbone and attack by Spinning when near to destroy the vertebrates one by one. Just watch out for the skeletons that pop out of the ground, as they'll act like pinball bumpers preventing you from getting to the boss. After three vertebrates are destroyed, the boss be reduced to a mere skull.

Raise a pillar in the center with the spinner. After which, the skull will come to life and knock you off the platform. There are two tracks: one around the center column and the other on the outside of the arena. You can hop between the two by pressing B. Hop onto the inside track and ride it back up to the boss. When you see him he'll begin to launch fireballs. Avoid them by jumping between the two tracks. Once he gets close, jump again to knock him to the ground and slash him with your sword. Spin attacks and jump strikes would work best (do the spin attack, and while it's recharging, keep doing jump strikes). After several attacks, he'll be defeated.

Blizzeta
When you use the Mirror Shard in Snowpeak Ruins, it will turn the kindly Yeti into a ferocious ice foe named Blizzeta.

Attack her with the ball and chain to shave off some ice with each impact. After several hits, she'll try a different tactic.