You can use a megaflip to skip the Big Octo fight, making Ruto useless after getting the Boomerang. You can then use a cutscene item (Zelda's Letter, beans, bottled item) on the first frame you land on the blue switch to keep the door open.
With a precise damage boost combined with a jumpslash, it is possible to skip the big octo. This method is considered glitchless. In order to also skip the blue switch glitchless, it is necessary to do a roll from a very specific spot on the switch and open the door on the right frame.
By dying while moving through a slimy tentacle, you do not receive knock-back which lets you pass through the slimy thing if revived by a fairy. If you do not pass through it quickly, you will take damage without invulnerability frames until you die once again.