The Mired in Muck side quest in The Legend of Zelda: Tears of the Kingdom can be found by interacting with Bazz at the Upland Zorana Skyview Tower. You’ll find him stuck in the sludge, unable to move. To free him, you’ll need to splash some water on the sludge to make it disappear.
If you have a weapon with a hydrant attached you can use that. Alternatively, there will be some Slash Fruit growing nearby. Pick some of those then attach it to an arrow and shoot it at the sludge. This will wash it away! The Blue Chuchu Jelly will also have the same effect.
Once freed, speak with Bazz. As a reward, you’ll receive a Zora Spear! If your inventory is full, you won’t be able to receive this new weapon. Once you have the weapon, the quest will complete!