The Mighty Octostomp's kettle can be found in the center of Octo Valley's Area 1. It rests on a large, purple pillow and does not need to be sprayed with ink to become visible.
You will start off in the Octostomp's lair on a platform with a spawn point and a launcher straight ahead of you. This is simply a small, safe place to prepare for the fight ahead, so there is not anything to do other than blast off to the main platform and start the fight. While in midair, you are given a view of the arena you have to fight on. It is a large circle with a podium towards the back and strong floodlights all aimed at the center. When you land, you are given a couple of seconds to see the arena from a ground perspective before the screen fades to black automatically and a cutscene begins.
You will be thrown straight into the action as the camera goes back behind you and the large pink-faced cube ahead charges in your direction. While you may want to shoot it, this will not actually do anything. The Octostomp will scream and then jump ahead trying to crush you, so make use of your own ink to swim and avoid it. As it lands on its face in an attempt to crush you, the Octostomp will spray its own ink around it, so be careful not to get stuck there and waste time.
While it is stuck on its face, shoot your ink up its side and use your squid form to get on top of it. Here, you will find a large tentacle sticking out of its back. Shoot the tentacle with your ink and it will expand multiple times until it eventually explodes, forcing you to retreat automatically via Super Jump to a safe part of the arena. The Octostomp will then re-grow the tentacle in its back and jump onto its feet before turning around and causing some of the metal plates on its side to fall off. The Octostomp will let out a cry, removing all the ink on the ground as the fight continues.
Like before, shooting the Octostomp in the face will be ineffective, so wait for it to jump, avoid it, and aim to climb onto its back once it gets stuck. This time, however, there will be open gaps in its side. Now you will have to take a chicane upward, avoiding the electric currents coming from the gaps. The Octostomp will also get up more quickly now, leaving you less time to get to the top before it rolls back onto its feet. When you manage to climb up, shoot the tentacle until it explodes like before. Again, you will automatically Super Jump back to a safe area.
The third phase is mostly like the second, but the Octostomp will lose even more panels from its side, meaning you will have to get across three diagonal squares to reach the top; the two on the sides moving up and down and the middle one staying in place. This orientation is rotated 90 degrees when the Octostomp attacks, meaning the moving panels move laterally instead of vertically. The Octostomp lets out a cry, the ink is removed, and the battle continues.
The Octostomp gets an upgrade to its attack — it still screams before jumping, but now it turns to face you right before the jump, making its attacks harder to avoid. Once it has jumped onto its face again, the best way to traverse the side is to cover all three panels in ink, go into squid form on the first panel and wait for it to be in line with the middle panel before moving onto it. Then, wait until the third panel is in line with the middle one, move onto that, then destroy the tentacle for the third time. It is possible to swim up all three panels in a single maneuver.
At the conclusion of the fight, The Mighty Octostomp explodes, throwing ink everywhere and covering the screen. After the ink clears, you will be rewarded with ten Power Eggs circling the Zapfish right in front of you. Collect the Power Eggs and the Sunken Scroll, destroy the lightbulb the Zapfish is stuck in, and retrieve it. Mission complete!