First of all, let's start by taking control of the beast: towards the end of the first room (1) where corruption awaits you. Uncheck an arrow in the water eye on the right (2), then lift the door with Cryonis (3). By passing the Sheikah tablet over the checkpoint, you will take control of the Ruta trunk.
Terminal 1
For the first terminal, return to the first room and examine the gears on one of the walls. Take Magnesis, grasp the handle with it, then turn until the device (5) is raised.
Terminal 2
Now go upstairs out through the balcony next to the first terminal, clean up the corruption that is keeping you from progressing. Once you are in the second part of Ruta (6), wait until the wheel activated by the fountain brings the terminal to a good angle, then turn off the water supply to stop the wheel (7&8).
Terminal 3
Place the Ruta trunk as high as possible to activate the giant gear placed just next to the second terminal (9), then climb on one of its blades to reach a small footbridge on your left. Here, you will have to wait until the ball falls on the pivot, then freeze it in this position at the very last moment (10) in order to leave the door open so you can reach the terminal in time.
Terminal 4
Now head for the Ruta trunk through the north exit of the dungeon. Before climbing on it, place it as low as possible (11) and then jump with the glider to the end of the latter (12). Now that you are on the ledge, make it go up very high (13) following the inclination until you finish on the other side, the fourth terminal awaits you there (14). Do not jump from here right away, the fifth one is not far.
Terminal 5
Look behind you: you can see the top of Ruta's head. Jump on it, then sneak through the small skylight (15). In this new room, a crank handle to activate thanks to Stasis: turn it until the opening is large enough to let the water from the trunk pass through (16). Tilt it as shown in picture 17, this will extinguish the flames and give you access to the last terminal in the dungeon.
Boss
Now that everything is activated, return to the ground floor, in the large back room, to validate the activation of the terminals, which will invoke Ganon's water shadow. During its first phase, it will only throw its spear at you or will give you shots that are very easy to anticipate and therefore perfect for timid dodges. In mid-life, the boss will raise the water and throw blocks of ice at you: destroy them as you go along thanks to Cryonis and in the lulls, untick a few arrows in the boss' head.
Written by Bastien "Lloyd" Dubosq-Luyer. Translated from French by Millenium.us.org.