After you activate the four faucets in the Water Temple, Mucktorok attacks.
The shark will sometimes stop and create a wave of sludge that goes outward in a circle. The shark can also shoot a beam of sludge in a straight line in front of it. Be prepared to jump to avoid these attacks.
Talk to Sidon to get a water bubble, then swing your weapon in the direction of the shark. You can also throw Splash Fruit or attach Splash Fruit to an arrow. Another option is to fuse an Opal to a weapon, and swing the weapon. When the shark is stunned, wait for Mucktorok to appear out of the sludge, then hit it repeatedly.
After Mucktorok's health reaches about 50%, there will be a cutscene, and Mucktorok will cover the platform with many puddles of sludge. Quickly talk to Sidon to get a water bubble and swing your weapon to clear away the sludge near you. Use Splash Fruit while Sidon recharges his ability, or a weapon fused with an Opal. Then use Sidon's water bubbles, or Splash Fruit, or an Opal weapon, to hit the shark when it gets close.
However, Mucktorok can escape into the puddles of sludge. To stop it, jump upward and then draw your bow to slow time, and hit Mucktorok with an arrow. This will stun Mucktorok so you can rush in and attack it before it creates its shark again.
After the Battle
There is a Heart Container for you to take after the battle. Talk to Sidon and there will be a cutscene.
Afterward, you will be back in Zora's Domain. This completes the quest.
If you have done the quest Impa and the Geoglyphs and started The Dragon's Tears, you will find Impa and Cado nearby. They can tell you more about Geoglyphs that you haven't found yet. Read The Dragon's Tears for more information.
You can also return to Lookout Landing, where you might find some clues about where to go next for the Regional Phenomena quests. See the following links for more information:
While in Lookout Landing, if you have completed Camera Work in the Depths but you haven't started A Mystery in the Depths, you can talk to Josha, and she gives you some Giant Brightbloom Seeds and arrows. This starts the quest A Mystery in the Depths.
Also in Lookout Landing, if you have completed at least two Temples, you can talk to Karson to start the side quest The Incomplete Stable. There is a plank next to Karson that fits perfectly, so use Ultrahand to put it in the gap in the stable roof to complete the quest. After that, you can talk to Lester to use the stable services.
After Regional Phenomena
If you have completed all four Regional Phenomena quests, go to Lookout Landing and climb the ladders to get onto the roof of Purah's lab. Talk to her there, and there will be a cutscene. This completes the Regional Phenomena quest. Your goal now is to enter Hyrule Castle.