In the room immediately after Makar's capture (the one with the WGA stone & spinners), go down to the first spinner. Immediately after using your deku leaf, backflip. You should hit the spinning wall as it's swinging upwards, taking you with it. Using this technique, we only have to spin it once.
In the room with Makar's cage, you can gain early access to the warp jar by shooting it with a Fire Arrow to skip some rooms. Use the warp jar in the first room of the dungeon to get up onto the ledge.
After Makar is used to plant the trees in both the room before and the room of his capture, he is no longer needed to complete the rest of the dungeon. This is mainly due to the fact that bomb ledge clips can be used to surpass walls and barriers that Makar would otherwise be required to clip through. The tricks below aid in skipping Makar.
In the room where Makar's cage is located, it is possible to clip through the walls and bypass the fan cage using a ledge clip. You can either use:
Either way, align yourself with the ledge you have chosen and hover to it. Backwalk so that Link grabs the ledge, move as close to the wall as possible, and then pull yourself up. Now use a bomb to ledge clip OoB. From here, glide to the mini-boss room loading zone. (Note: If you are using the first ledge, after you clip you will have to wind waker dive using a bomb to push you in order to bypass the death trigger so you can reach the loading zone.)
This method is best done after using the Fire Arrow Trick to open the warp jar on the upper ledge. Once you've opened the first fan cage, jump down to the highest platform on the right. Kill any peahats that may interfere, place a bomb, and ledge clip OoB. Note that in order to clip, you must press the control stick away from the wall as soon as you re-grab the ledge (review video for reference). Immediately after Link slides through the wall, drop down onto the lower ledge. Now simply glide to the hookshot room and you will hit the loading zone.
Note: Compared to the above method, you do not need to use a bomb push wind waker dive after you clip, as you are a lot lower down and therefore the death trigger should not be an issue.
Get into one of the corners near the spikes and place a bomb--it doesn't matter if it is in front of, or behind you. Wait until just before the bomb explodes and use a damage boost to reach the spike ledge. (If you placed the bomb in front of yourself you will need to jumpslash a second or two sooner.) This will give you temporary damage invincibility as well, allowing you to then skip past the spikes and get to the chest.
After you have obtained the small key above and the hookshot, head over to the right of the key room and hookshot up about three platforms. Backwalk so that Link grabs the ledge, move as close to the wall as you can, and then pull yourself up. Now place a bomb and use it to ledge clip OoB. Immediately after you've clipped and drop down onto the lower ledge. From here, backflip off the ledge and use the leaf to get under the second fan cage. Be careful not to fall too far or you will die.
The room with the wall of wind gusts where you'd normally have to use Makar to plant a tree and then hookshot it, can be crossed without the aid of Makar. Jump into the wind gusts and pull out the deku leaf to get blown left and then right. As soon as you are in front of the platform, put away the deku leaf and hold forward on the control stick to grab the edge.
In the room before the boss door, you can skip pushing the blocks by putting on the iron boots and continuously sidehopping past the blade traps.
Get next to the stone slab and sidle. Once Link is part way in the stone, stop sidling and roll until you are completely through. To get through with the fewest rolls possible, roll parallel to the stone.
Make sure that you've called Tingle and diminish your health to 1/4 of a heart. Position yourself so that you're facing a bot right of the boss door. Now kill yourself and hover up above the frame of the boss door and heal yourself with a red ting. You must be sure not to be too high above the door when you get healed, otherwise your sword will simply bounce off the wall and you'll miss the door frame altogether. Once you're on the door frame, walk to the end of one side (it doesn't matter which) until Link grabs the ledge. Now simply ledge clip off a bomb and jump into the loading zone.
If for one reason or another you don't have access to the Tingle Tuner, you can still preform this dungeon's boss key skip. To do this, pick up the middle pot on the right side of the room and break it near the boss door. Zombie hover above the door frame and make sure to stay low. If you're lucky, as the fairies ascend, one of them will heal you.