It never hurts to watch videos of other people going through this challenge. Don't worry about fast times, just survive. Know when you can use your shield and use it wisely. No matter how good you are, you will always take cheap hits. If you're only going through 8 of the bosses, avoid the horde battle, as it seems to give most players the most trouble; however if you eventually try to go for all 12, do this first and get it out of the way. Always look for the easier ways of damaging the bosses, don't take a more difficult chance to do damage if you know you're more likely to take damage yourself.
When you're fighting Girahim, you can usually use your shield against most of his attacks. The flying daggers can be easily deflected this way, but in the 2nd battle when he surrounds you with them, shielding is useless. Avoid engaging him close up in the 2nd phase of the 3rd battle, or you're going to get murdered; instead wait for his "skyward strike" and play ping-pong like you would with Phantom Ganon.
Against the Imprisoned, you can jump on his head and hit the spike from there. In the 2nd and 3rd battles you have to stun him with the Groosenator before trying this, or he'll just throw you off. You could also use well-placed skyward strikes to slash at his toes if you don't want to get to close to them.
Against bigger bosses like Scaldera, Moldarach, Koloktos, and Tentallus, it's easy to take cheap hits. Always stay on the offensive with Scaldera, don't give him time to attack, just pelt him with bombs at the right time. Realize when Moldarach is attacking: the eye (either in his head or claws) turns read when he's about to attack. Either take that chance to strike the red part quickly or dodge the attack and not risk loss of precious hearts. A tense note plays in the background right when Koloktos attacks, dodge accordingly whenever you hear it. When Tentallus is under the ship, don't stop moving or one of the tentacles can easily damage you. Between phases, pay attention to the barrels, as you can take cheap hits just trying to climb up.
In the horde battle, just run. You don't have to fight everything. You do, however, have to fight what appears whenever a wall blocks your path, only when those specific monsters are defeated can you move on. Use spin attacks sparingly: they can hit a lot of enemies at once, but it takes a toll on your energy when you'll be doing a lot of running.
Against Demise, for goodness's sake, SHIELD! Shielding and backflipping can be used against nearly every attack to avoid damage. In the 2nd phase, take every opportunity to charge your sword, but pay attention and be ready to defend yourself.