Read how to kill the Great Colored Carp on location Palace Grounds.
When you are in the Palace Grounds, first go ahead and kill the Corrupted Monk. Get down, but do not rush to swim in the water, because the enemy will shoot at you on a huge tree on the other side. Move through the buildings on the left, go through the Mibu Village and exit to the bridge. Walk forward to see the Great Colored Carp, which will destroy the bridge. Jump over to the other side, clear a large location from the enemies and get to the big tree. Kill the mini-boss, the head of the clan. Jump into the water and swim back. There is a woman on the roof of the sunken house. Chat with her to find out about the cave.
Jump into the water and swim along the bottom to the rock. Downstairs will be a ruined building. Swim into the cave to the left. Hide from Carp, swim to the other end through a hole in the sunken building. Get outside and see the idol "Palace". Pass into the building, turn to the right and open the door at the chest. Go right to jump onto the roof of the same building. From the left nearest corner you will need to jump to the right of the mountain (that is, in the wrong direction, where the idol is located). You will be hooked on the branch, move to the roof of building and kill enemy. Jump down and go to the water to find the father of the old woman. He is forced to feed carp for eternity. Use the bell to summon the carp.
Feed it with food. You can find him at the Guardian Ape’s Watering Hole (where they fought with the boss), or in one of the parts of the Palace Grounds. Once fed, return to the Dragonspring Idol in the Hirata Estate. Jump into the water and swim to the island to the right. Talk to the merchant in the barrel (you will first need to buy something from him for the scales), so that he gave you Truly Precious Bait.
Feed the Great Carp with it, then move to the Guardian Ape’s Watering Hole and see that the carp lies here. He is dead. Pick up item. Show it the old man who was forced to feed Carp. Also visit a merchant in a barrel in the river at the Hirata Estate to get the new item - Lapis Lazuli. This item is needed for advanced prosthetic enhancements.
Note. In the Palace Grounds you can find another merchant in the barrel. Take the Truly Precious Bait from him. Kill the Great Carp and you will help this merchant. He will turn into small Carp. In any case, there will be only one of the merchants, and the range of goods of the missing person will go to him.