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.
With chest storage, you can enter Forbidden Woods by running up the island. You cannot get up onto the island from the water however, you need to leaf to it from either KoRL or from another island. Because of that, the strategy above is more commonly used.
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.
It is possible to kill blue flowers faster using two well-spaced bombs than with a single bomb, as you can slash the second bomb to cause a chain reaction that kills the vulnerable blue flower.
Using chest storage on the map chest, it is possible to get to the treasure chart while skipping almost every bulb. Unfortunately this breaks even with doing the room normally, thus isn't done in speedruns.
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.
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.
If you have the tingle tuner activated and don't need to reveal the warp pot, you can use a tingle balloon in the main room to skip leafing to the blue flower, saving some time.
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 method above.
Immediately target the Mothula and maneuver Link over to the barred entrance door. This is easily done by holding ZL, Up on the left control stick, and Down on the right control stick. Right after the Mothula is at the peak of it's hovering oscillation, use the Leaf to blow a wind gust and stun the enemy. The delay caused by Link's animation will make the gust stun the Mothula at the lowest level of it's oscillation cycle. From here maneuver Link to the other side of the Mothula, placing it between Link and the door. After it slowly falls for about three seconds do four separate stabs to take off the wings and ground it (separate the stabs enough so that Link doesn't do the stab combo). After the Mothula is grounded, it has eight health. Ideally you can do two quickspins with the Mothula now cornered in a wall with each quickspin hitting twice.
You'll encounter Mothulas later in any speedrun of TWW. In almost all of these cases, you'll already have the bow and ice arrows. For grounded Mothulas you can simply kill them with a single bow shot or by pounding them with the hammer, and flying Mothulas can be quickly eliminated with a single ice arrow shot.
After defeating the miniboss, if you got the bombs early, you can store the boomerang chest to both obtain the boomerang and get chest storage. With chest storage, you can activate the loading zone to leave the room by simply hugging the door, skipping having to aim the boomerang at the switches to unlock the door.
Target all the vines that holds the Big Blue Flower to the ceiling with the boomerang and throw it. While the boomerang is cutting the vines for you, jump forward to drop all the way to the basement while the cutscene of the big blue flower dropping down is happenening.
It is impossible to cut the Big Blue Flower early in order to go to the basement without the boomerang, since the game checks for you having the bomerang in your inventory for the cutscene of the flower dropping to trigger. It is however possible to go to the basement early thanks to a few tricks:
You can use the nut or a bomb in order to legde clip OoB where the warp pot is located. From there, you can drop into the water and even go under the water and to the basement early.
In the Morth Pit room, store the door leading to the vine maze and then open the door leading to the main room. This will load both rooms at the same time while unloading the room you are in. Now that you are OoB, you can simply glide under the floor and into the basement. Be careful as to not drop too low at once or else you will void-out.
By hanging off the ledge on the left side after entering the flower sailing room and letting go of it, it is possible to clip OoB and clip back past the wooden gate. This clip is rather unique. This is usually not a time saving trick.
First, make sure to open the door leading to the room containing the treasure chart in the middle. Right after entering the room, pull out the boomerang and aim slightly left of the the hollow tree, at middle height. Then throw the boomerang, press target to make the camera stop focusing on the thrown boomerang, and run towards the platform on your right. The boomerang will try to come back to you and because it goes through everything when it's on its way back, it will go through the hollow tree and destroy the spiky flower protecting the chest containing the chart. This trick skips having to maneuver all the way to the bomb flower at the top of the room.
If you got the bombs early, then this is a much smaller timesave.
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.
It is possible to simply walk into the hollow tree containing the Big Key Chest with Chest Storage.
You can also get the big key early using the hookshot. There is indeed a gap in between the floor and the gate preventing you from accessing the chest. The hookshot can target the chest via that gap to skip the boomerang requirement. Note that this is technically never useful.
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.