You can easily get the pictobox from Koume and skip having to ride the boat to Deku Palace just like in the original Majora's Mask. Just stand next to the door and target Koume, talk to her and mash A to open the door.
By performing a long jump from the flower next to the big octo you can land ontop of the stone, quickly transform into Deku Link and you will get thrown away, just void out from the water, go farther to the corner to get thrown away again and after voiding out make a sidehop to skip the big octo then let the other octo on the other side to throw you away and land on a lily pad.
When Deku Link drowns in water and respawns, he has a couple of invincibility frames before anything can hurt Link again. While the invincibility frames won't damage Link, he'll still receive knockback from the enemy or object that would usually hurt him. By using this knockback (otherwise known as Megaflip), Link can get thrown and land on a part of the rock platform. If you fall from the platform, which is really easy to fall off from because of where you landed, just drown again and Link will respawn on top of the rock again. From there get thrown out again and like the method above (With Explosives) just sidehop off to the right onto the lily pad.
The developers fixed the little roof on the swamp house by making an invisible wall so you can't clip through with a Goron Pound like in the original. But they only fixed that for the Poisoned Version of the swamp, they forgot to do the same for the Clean Version of the swamp, meaning that you can do a Goron Pound and clip through the little roof and landing on-top of the house leading to the heart piece skipping having to get the Land Title Deed from the Business Scrub in Clock Town.
Using Extended Hookshot, you can hookshot all the way to next to the entrance of Woodfall, not having to bother using the deku flowers and/or the long jumps with Zora.