Get on the wall on the left side of the castle and pull out the boomerang. Aim above the rectangular hedge and throw the boomerang. As it is coming back to you, do a Long Jump Attack to get on top of the hedge. From here you can simply open the door to the next area and avoid the barrier/cutscene trigger.
From the main entrance to the Hyrule Castle courtyard, head over to the left (GCN). Stand near the bush wall, and lure a Kargaroc to come near you. Use an attack to knock the Kargaroc on the other side of the bush wall, and target him with an area attack. Back up a bit, and use the the area attack to super jump over the bush wall and past the barrier.
In the first room of Hyrule Castle, head to the middle of the room to cause the barrier to form. Head over to the right side (GCN) and wait for the group of bokoblins to appear. Just as they enter the barrier, hit the first one with a shield attack and use the helm splitter to jump over the barrier.
When Zelda tries to throw a ball of energy at you, get under her and use a quick spin, or regular spin attack, to knock it back at her. Instead of trying to rally it back and forth, it will hit her immediately.
Turn into a wolf and wait for Ganon to charge you. When he does, grab him and throw him to one side. Use a jump attack - spin attack combo on the slash on his belly to finish him in three cycles.
Follow Ganondorf closely and hit him with a light arrow, followed by a spin attack. Immediately after hitting him, continue to follow his movements accurately and hit him with another light arrow. If you do this properly, it will prevent Ganondorf from summoning any of his Phantom Riders.
Run at Ganondorf without targeting him, and use a sword slash. Ganondorf will simply block it, but this gives you time to get behind him and hit him with a jump attack - spin combo. Get behind him before he gets back up and use another jump attack - spin combo. Repeat this process and after the third time press A to finish.