When you go back to report to Sidon at Mipha Court, a Sludge Like attacks.

Complete Clues to the Sky

Before you can battle the Sludge Like, you need to complete the main quest Clues to the Sky, then go to Ihen-a Shrine and talk to Sidon.

Take a Picture

If you have completed the quest Camera Work in the Depths, you can take a picture of the Sludge Like for the Hyrule Compendium.

Use Sidon's Power

Talk to Sidon to surround yourself with a bubble of water. Dodge the Sludge Like's attacks to avoid letting your water bubble disappear. Then when the Sludge Like stops its attacks, swing your weapon to hit it with a blast of water. Another option is to throw Splash Fruit at it, or fuse an Opal to a weapon.

After you hit the Sludge Like with water, wait for the Sludge Like to stick its tongue out, and shoot the tongue with an arrow to stun the Sludge Like. Then you can swing your weapon at the tongue repeatedly.

After your attack, the Sludge Like will disappear into another puddle of sludge. Talk to Sidon to surround yourself with another bubble of water, or throw Splash Fruit or use an Opal-fused weapon, and repeat the strategy as described above.

After the battle, be sure to open the chest that the Sludge Like dropped, to get a Royal Claymore.

Now that the Sludge Like is gone, you can go south to the quest location to find Sidon. Talk to him and he will open the way to the Ancient Zora Waterworks.