After reaching Zora's Domain and using shock arrows to open the way, you reach the interior of Divine Beast Vah Ruta.
Get the Map
You will be told to look for the map first, and will be shown where it is. Go through the entrance door and use an arrow to shoot the orange eye in the Malice goo. This will get rid of the nearby goo.
When you go past where the goo was, a Guardian Scout attacks. Guardian shields and weapons are more effective against these than other equipment, so use these if you have any. The simplest way to kill it is to do a perfect guard: hold ZL to raise your shield, then press A (not Y) just before its energy blast hits you, so that you reflect the energy back to the Guardian Scout, killing it.
Then go over to the nearby water and look for the orange eyeball below the water's surface. Shoot it with an arrow to remove the Malice goo from this area.
Use Cryonis under the bars to raise them. Then go past the bars and check on the guidance stone to get the map of Vah Ruta. In the map, you can adjust the position of Vah Ruta's trunk, which will spray water into the interior of the Divine Beast at different locations. You will need to do this later.
For now, you can check the map to see the orange spots that indicate where you will find a terminal. You need to find and reactivate all five terminals before you will be able to regain control of the Divine Beast.
Get a Treasure Chest
Before you continue, go past the bars that had been blocking this room, then use Magnesis to pull up the treasure chest that is in the water here.
Activate the First Terminal
Across from the room where you got the map, there are gears on the wall. Use Magnesis to rotate the gears to raise the terminal from the water. Check on the Guidance Stone to activate it.
Activate the Second Terminal
There is a door near the bars that led to the map. Go through that door and go up the ramp. Go through the door at the top of the ramp. There is a Guardian Scout here, so kill it.
Near where the Guardian Scout was, there is a rotating waterwheel, and there is a terminal inside of it. Wait for the terminal to rotate to the bottom of the wheel, then use Cryonis on the place where the water is coming out that is pouring on the waterwheel. This will stop the wheel, and you can go down into the waterwheel to activate the second terminal.
Get a Second Treasure Chest
There is a treasure chest on the ledge behind the water spout that you froze. You can reach it by shattering the ice pillar that you created in the water spout, then swimming onto one of the teeth of the waterwheel and riding the wheel to the top, then gliding to the treasure chest. Just be careful not to step on the Malice goo that is on some of the waterwheel's teeth.
Get a Third Treasure Chest
Go into the map and choose the fourth purple mark from the top, then press B to make Vah Ruta move its trunk. Water will pour from above, making the second waterwheel begin to turn. Stand near the larger waterwheel and look for an orange eyeball on the underside of one of the waterwheel's teeth. Shoot it with an arrow. This uncovers a treasure chest that is stuck to the tooth of the waterwheel where the eyeball was. After the treasure chest goes past, walk onto the next tooth of the waterwheel, then ride the wheel up until you are able to open the treasure chest.
Activate the Third Terminal
After that, you will be facing a ledge to an upper level. Glide through the water pouring from above to land on that ledge. There is a Guardian Scout here, so kill it.
You can step on the switch nearby to turn on a waterfall that will allow you to quickly come back to this upper level using the Zora Armor.
There is a raised walkway that goes into the nearest waterwheel. You can see it from the switch that you just stepped on. Glide onto that raised walkway, then walk toward the center of the waterwheel. You can see a small room in the wheel that contains the next terminal. This room is blocked by bars unless the orange ball is in the target hole at the center of the waterwheel. The ball will slide away from the target hole as the wheel turns, so you need to use Stasis on the ball just before it starts to slide away from the center. When you freeze the ball, make sure that you are still standing on the raised walkway that leads to the center of the waterwheel. After freezing the ball, wait for the room to rotate so you can walk into it and activate the third terminal. The bars will not close anymore after you activate this terminal.
Get a Fourth Treasure Chest
Go back onto the walkway and look at the waterwheel. There are are two large blocks that slide as the wheel turns, and there is a treasure chest on one of those blocks. When the blocks have slid away from the center of the wheel, wait until they are just about to slide back to the center of the wheel, then freeze the outer block. After the wheel rotates some more, the treasure chest will slide to the center of the wheel and you can open it before the outer block slides back down.
Get a Fifth and Sixth Treasure Chest
There is a door near where you stepped on the switch to activate the waterfall. Glide down to the waterfall and use the Zora Armor to swim upward in it. When you automatically take out your paraglider above the waterfall, you can float to a ledge with a treasure chest. Then go back to the ledge just above the waterfall that you swam up, which has the activated switch just above the waterfall. Go through the door near that switch.
At the end of the hallway, you find Vah Ruta's trunk. Use the map to select the lowest purple mark, then press B to move the trunk. Walk along the trunk and shoot the orange eyeball. You can try to shoot it from a distance to avoid making the Malice mouth spit skulls at you. After you kill the eyeball, you can reach the treasure chest.
Activate the Fourth Terminal
While standing where you opened the treasure chest on the trunk, raise the trunk to a high position (to at least the middle setting if not higher) and wait until you are high up enough to glide down into the hallway that you came from a moment ago. Then while in the hallway, lower the trunk to the lowest position, and when it has gone all the way down, glide to the platform near the very end of the trunk.
There is a terminal on the very end of the trunk. To reach it, raise the trunk to the fourth mark from the top, and walk toward the end of the trunk as it goes up, walking on the water spout and carefully past it, until you are able to activate the fourth terminal.
Get a Seventh Treasure Chest
If you look toward Vah Ruta's body from here, you will see some areas with Malice goo on them. Float to the area on the left, then look at the opposite side and shoot the orange eye there. The Malice goo will disappear and you can open the treasure chest.
Activate the Fifth Terminal
Look between the falling water and Vah Ruta's trunk. There is a platform with a small square hole in it. Float there and fall through the hole. When you land, shoot the eyeball in the ceiling. Get rid of any skulls that the Malice goo spat at you (if any), then use Magnesis on the crank on the wall to open the ceiling.
Move the trunk to the fifth mark from the top. Vah Ruta's water will pour onto the flames below, making the fifth terminal accessible. Float down to it and activate it.
Get a Treasure Chest If You Missed It
From the fifth terminal, go toward the new orange mark on your map, but be sure to open the treasure chest just below the ledge where you activated the fifth terminal, if you didn't open it earlier.
Activate the Main Control Unit
From here, go back to the lowest level of the Divine Beast, on the level where you got the map. There is a ramp next to the gears that you rotated to reveal the first terminal. Go down that ramp to reach the Main Control Unit. Get ready for a boss battle, then activate the Main Control Unit.