If you go through the exit the game normally expects you to go through after getting the Leaf, you can Item Slide into the entrance of Forbidden Woods by backing up against the left wall, charging a slide against it, and then slashing forward. Unlike what the video says, holding Up is not required when buffering the slash.
Sail to where the cyclone is, near the tree between Forest Haven and the Forbidden Woods. When it's next to you, jump and use deku leaf. It will lift you up and land you on the tree. Wait for the cyclone to move and 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 room with the baba buds and tentacles, it is possible to skip one of the 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 higher platform that is near the door. At least two pumps are necessary.
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.
There are multiple rooms in the Forbidden Woods where there are moving cable platforms that normally need to have a gust of wind blown at a nearby pinwheel to be moved. Instead, a much faster method to get across the room is to glide towards the platform, 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 use a leaf pump or two to get to the ledge.
It is possible to make an earlier platform cycle on the roots leading to the covered warp pot by jumpslashing onto the higher ledge before the grapple spot and Item Sliding across to the platform in front of the door with the blue flower. If you are quick enough, you can jump onto the lower platform before it moves up and throw a bomb down at the blue flower before using the leaf to reveal the warp pot.
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 three methods.
It's possible to Item Slide past the tentacles in this room by charging up backward against the door, then releasing your speed with a forward sword slash. Aim between the baba bud and the wooden barrier to the left of it for this trick. If performed correctly, you should clear the tentacles before they even come up in front of you. If you get hit, you either weren't travelling fast enough, or you were aimed too far left or too far right.
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.
Diminish your health to 1/4 heart. Position yourself facing the high ledge, and place a bomb in front of yourself. Zombie hover off the bomb and drop another bomb using the leaf once you are above the ledge. Hopefully, the bomb will blow up the grass and produce a heart drop to heal you. Proceed to the next room. cut the pine cone, and deku leaf over to the far ledge (leaf pumping will help). Proceed to the mini-boss battle.
Note: This method is inconsistent due to requiring an RNG heart drop.
Jump down to the floor on the right side of the room and charge an Item Slide back against the wall. Release the speed with a forward slash to jump and use the leaf to turn and fly towards the ledge on the other side of the room. Leaf Pumps will usually be required.
With a sideways Item Slide that is lined up parallel to the outside wall of the alcove that protects the boss key, you can clip through and obtain the boss key without having to solve the boomerang puzzle.
Diminish your health to 1/4 heart, then throw the deku nut that has a fairy in it forward and kill yourself with a bomb. Hover up the right side of the boss door structure and get healed by the fairy when you reach the top. Now backflip and leaf to the ledge so that you grab it partially within the wall and do a roll clip to get out of bounds. Then just fly over the loading zone with the leaf.