The Orca fight contains a few tricks that will speed it up by a few seconds.
During the first phase of his training, you will need to perform 3 combos (the normal combo, the holding target combo and the stab combo). However, instead of performing these combos normally, you can instead start holding back on your control stick before your 3rd hit, and holding forward on the control stick before the 4th hit. This will make you do a combo that ends with a spin attack instead, which is faster.
Then, Orca will want to you to perform a spin attack. Perform a quickspin by doing a full circle on your control stick before pressing b, which is faster than doing a spin attack by holding the b button.
Then comes the parry attack. Target Orca and wait until the arrow above his head goes up for its 4th time. Then press A to parry him. If you parry Orca on either the first or the second possible frame, his second parry will come instantly after the first one, saving 4 seconds. In the HD version, because Orca doesn't send you on the floor if you don't do the correct attack, you will still get the instant parry if you parry him slightly early.
Finally you will need to perform two jumpslashes. You can perform a very slightly faster jumpslash on the 2nd one by sidehopping and pressing b to do a fast mid-air jumpslash.
If you don't have a sword, then there will be an invisible wall behind the trees preventing you from accessing the Forest of Fairies early. However, that invisible wall doesn't extend onto the ledge on the left side. With enough speed, it is possible to land onto that ledge and avoid the invisible wall alltogether. To reach the speed necessary, you can either use superswimming speed, or use item sliding. The video below shows a setup to enter the Forest of Fairies with item sliding that doesn't involve having perfect speed:
If you picked up the gossip stone in FF1, then the bridge leading to FoF will be broken. It is however possible to item slide accross the broken bridge as seen in the first video.
The same trick as above is possible without the grappling hook by using a superswim instead, although it is harder. Make sure to not have picked the gossip stone before or else the bridge on top of Outset will be broken.
Entering the forest early is very easy with the deku leaf: simply jump onto the roof of Mesa's house and leaf to the ledge. This avoids the invisible wall completely.
Entering FoF early can be very important depending on the route. If you don't save Tetra in the forest normally, by performing Outset Escape to skip it, entering the forest later in the game can have unpleasant results. If you haven't saved Tetra, and if you enter FoF either during night, or after FF1, then the game will simply crash no matter what, which can prevent you from ever obtaining the last wallet upgrade. If you wish on not saving Tetra in a 100% speedrun, then you must obtain that wallet upgrade before beating FF1 and during the day.
If you perform the Flight Control Platform Escape glitch, and then superswim to Outset, you will notice that the Pirate Ship is there on Outset, in the location it would be after saving Tetra in the forest during the prologue. If you have a sword, you can simply item slide backwards into the corner near Grandma's house, aim at the pirate ship and slash your sword to get on top of it.
If you didn't obtain the Gossip Stone in FF1, Outset will still be in its prologue state. If you've watched the cutscene of Helmaroc coming to Outset during the Prologue, the pirate ship will be on Outset in a different location than in the video above. It is possible to item slide into that pirate ship using the same technique. If you don't have a sword, you can do the setup below:
Since this 2nd method requires not having the Gossip Stone, it is only useful in order to obtain the Spoils Bag from the pirate ship. See the Pirate Ship Flags for more info.
By getting damaged by the fire and then quickly using the Hookshot on the torch, you can enter the hole before the temporary damage invincibility wears off. This trick can be performed on floors 21-29 as well as any other floors with torches. The Iron Boots can also be used in order to minimize the distance of the knockback from the fire so that it is easier to enter the hole with the Hookshot.
You can actually skip every single floor in savage labyrinth with a well positioned and precise Item Slide through the flames that block each grotto.
By item sliding against the Elephant Statue for long enough with the hookshot, you can get the camera to sink. As soon as the camera sinks, release the hookshot button to fire it and have the camera stay under the ground. This is called a Weirdshot. Now, hookshot one of the torches on either side. If your positionning is correct, you will get crushed by the elephant statue, causing the area to reload. This allows you to farm the rupees in the pots, being the fastest rupee farming method in TWWHD.