Sail to where the cyclone is by the tree in the water. When it's next to you, jump and use deku leaf. It will pull you up and land on the tree. Wait for the cyclone to go around and deku leaf to Forbidden Woods. It is also possible, but more difficult, to sail around to the opposite side of the tree, wait for the cyclone, then jump to it and glide directly to the Forbidden Woods without having to land on the tree and wait for the cyclone again.
In the next room of the dungeon, it is possible to skip one of the deku buds. Jump into the first bud and at the height of your expulsion, pull out the deku leaf and use leaf pumping to get the the higher platform that is near the door.
There are multiple rooms in the Forbidden Woods where then are moving cable platforms that you normally have to blow a gust of wind at a pinwheel to move towards you, jump on it, and then move toward the other side of the room. Instead, a much faster method to get across the room is to glide towards the platform and the put the deku leaf away just before you hit the platform to grab it, and then glide to the other side of the room.
Instead of grappling to the post to get by the tentacle, jump towards the platform and using a leaf pump or two to get to the ledge.
In the hanging flower room, it is possible to reveal the warp pot while waiting on the second rising platform to go up. While standing on the first rising platform, use the deku leaf to blow a gust of air at the slant on the second platform. The air gust should bounce off the platform and hit the warp pot from bellow.
In the room with the labyrinth of vine tentacles, it is possible to skip navigating your way through the maze after blowing up the wooden barricade blocking the key chest using one of two methods.
Get on the right side of the far right tentacle, the one near the tree, of the first row of tentacles blocking direct access to the key. Now align yourself at a slight angle with the tree and jumpslash. If done correctly, you should damage boost off of the tentacle, pushing you over their barrier.
Get by the same tentacle as in the previous method, but this time, simply run into the tentacle to take damage. This will give you temporary invincibility, as long as you are still flashing red, against taking more damage. Now you can simply roll through the space between the tree and the tentacle to skip the labyrinth.
Call tingle, then deminish your health to 1/4 heart. Position yourself so that you are facing the high ledge, and position the tingle icon in front of you. Zombie hover off of a tingle bomb, and heal yourself once you are above the ledge. Proceed to the next room and cut the pine cone, and deku leaf over to the far ledge (leaf pumping will help). Proceed to mini-boss battle.
Note: This method is used much less frequently than the following method.
Perform Dry Storage in the room with the three boko-babas, and get chest storage off the treasure chest in the tree. Proceed to the big flower room. After the grappling post, walk up the tree jutting out of the wall on the right. Sidehop at the highest point and leaf to the big flower. From there, blow open the warp pot and leaf to the right side of the bork as shown in the video. Glide to the wall between the two doorways, using chest storage to wall up to the top door. Jumpslash on the chest in the next room and leaf over to the other platform. Enter the mini boss room.
Make sure that you've called Tingle and go to the left in the room with the Morths on the log platforms. Zombie hover up to the ledge and then heal yourself. From here, you are free to make your way to the boss key. This trick is not used very often because of the time it takes to diminish your health after the early boomerang hover and the additional rupees required. For these reasons, the following trick is typically preferred.
Jump off the ledge towards the hanging flower but make sure not to land on it. After falling beneath it, pull out the deku leaf and begin leaf pumping down the tunnel. Because of the height the leaf pumping allows, you can just reach the ledge at the end of the tunnel.
Target all the ropes, then jump to the hole.
Perform storage and open the chest in the room before the small key (as shown in the video below). This will store opening the chest and its contents, allowing you to partially clip into walls. Head to the boss door and wedge yourself into the corner between the door and the wall. You should be able to easily squeeze past the boss door.
Note: Although forest water storage is hardly used due to the 20 minute time discrepancy and the discovery of dry storage, it would be of optimal use in an any% individual level speedrun. This is because you can time the forest water so it expires just after you get to the chest in the room with the two Mothulas. Early bombs will also allow you to bypass the blue flowers on doors without the need of the boomerang. More info on skipping the boomerang in the Forbidden Woods can be found here.