Temple of Droplets is one of the Dungeon that gets completely destroyed by the glitches you can use in here.
Thanks to Boss Door Clipping and the Ocarina Glitch, it is possible to completely skip the left and right side of the dungeon after getting the Boss Key.
The Lantern is still required, however, as there is no method to defeat the boss without it.
After getting the first small key, you can use the Ocarina Glitch to get the Boss Key without using a small key, saving it for the mini boss.
Using the Ocarina Glitch, it is possible to skip everything after the Lantern and go straight to the second lever to activate the boss.
Octo will always shoot boulders at you in his first phase.
In his second phase, the pattern is suck, boulder, suck, boulder, boulder and repeats that pattern until he's hit 3 times.
On his 3rd phase, it's completely RNG based:
After being hit by at least 1 boulder, his attack pattern will change a tiny bit once again:
Therefore, 2 ink is the most he can give you if you reflect all boulders he shoots at you.
There is also a manipulation possible for Big Octo to always get 0 ink on the third phase.
After obtaining the small key north of the entrance, do the Ocarina Glitch at the top of the stairs and head to the boss door, go up the stairs at the entrance of the dungeon and walk to the left or right of the boss door and into the next room.