Sekiro: Shadows Die Twice - GOTY Edition

Short version: In Fountainhead Palace at the Feeding Grounds idol - Ring the feeding bell and feed the great carp "truly precious bait". After he swims away, travel to the Guardian Ape's Watering Hole idol in the Sunken Valley area. Here you will find the carp's carcass along with his whiskers, netting you the achievement.

This is an extremely complicated achievement but I will do my best to include everything.

TLDR
1: Reach Fountainhead
2: Kill Lightning shooter atop the tree by the Great Sakura idol.
3: Grapple up to Merchant in a pot.
4: Purchase Mask Fragment for 12 Treasure Carp. (possibly own all 3 mask fragments).
5: Talk to him again to acquire "Truly Precious Bait".
6: Swim underwater through the cave, past the Great Carp, to Palace Grounds idol.
7: Grapple hook onto the roof, then tree, then left to reach Feeding Grounds.
8: Ring bell, feed him Truly Precious Bait.
9: Fast travel to Guardian Ape's Watering Hole. Collect Whiskers item.
10: Profit.

Long version: First off, find the Great Sakura idol and kill the enemy on the nearby tree who shoots lightning at you in the lake so that you can now safely swim around.

Then, from the third idol in fountainhead, Flower Viewing Stage, make your way up and toward the back of the area to a closed double door and a waterfall. Facing the door, there should be a waterfall to your left. Cross over this waterfall onto a grassy area with a tree. Looking at the tree you should see a Grapplehook mark on the rocks behind it and to the left a bit. You may have to move around some if it doesn't appear right away. Grapple up and go through to the next area where you will find the Near Pot Noble idol.

Next to the idol is a man in a pot. Talk to him and you can purchase the third Mask fragment. (Note: I already had the other two pieces in my possession, thus completing the mask. I am not positive if this is required or if simply buying the piece he is selling is enough.) Upon buying the mask fragment, talk to the npc and exhaust his dialogue. He will offer you a Truly Precious Bait to feed the great carp, which will kill him. Normal "precious bait" can be found elsewhere and only feeds him, it will not kill him. Only this "truly precious bait" will do the trick.

The Truly Precious Bait cost 12 Treasure Carp Scales. These can be found in any underwater area by killing the pink dolphin-looking fish. There are many in this area, some are also on the lake bottom appearing as items.

Now, as far as getting to the Feeding Grounds area, you must swim through an underwater cave in order to first reach the Palace Grounds idol. Start off at the Vermilion Bridge idol and step out to where you are overlooking the whole area. If you look in the middle of the lake, on the right hand side, there is a hut floating/sticking out of the lake. This is what you should aim for. When you reach the hut turn right and dive underwater. Eventually you should see the underwater cave on your left. Swim through, avoid the great carp, emerge on the other side to the Palace Grounds idol.

From here, enter the doors, turn right and go up the stairs, you will pass a chest on your right. Once outside again, immediately turn around to your right. You should see a grapplehook icon on the next building. Get up onto the roof and go to the far edge. Look up and to your left to see a tree branch sticking out. Grapple to this branch (running start advised) and then down to the rooftop below/left. Continue down in this direction to find the Feeding Grounds idol. You can speak to the man here, he will tell you to ring the bell to feed the great carp.

Ring the bell, select the Truly Precious Bait, Travel to Guardian Ape's Watering Hole.

I know this was very long and confusing. I will update as needed.

In this video guide I will show you how to defeat the Great Colored Carp. You won't be able to do this until you reach the Fountainhead Palace. You will need to follow several steps in order to do this achievement.

First you will need to kill the lightning mini boss on top of the huge tree next to the pond. Once you kill him you can go underwater can kill some fish for carp scales. If you haven't already saved carp scales you will need to find 12 of these to buy a mask fragment.

Next you will need go back up the stairs next to the idol on top of the tree. You will see a big locked door, now if you are facing the doors look to your left to see a waterfall. And just past that if you look up to the right side of the mountain and above the tree you will see a grapple point. Now just follow the path until you grapple down to a house. Once you jump down you will see a pot next to the tree. He will be the merchant that will sell you the mask fragment. Buy it then start talking to him to exhaust the dialog. Once you do he will ask you if you want to hear a tale, make sure you say yes. Once his story is finished you will receive truly precious bate. You will need this to feed to the great carp.

Now if you haven't already you will need to swim in the pond and go through where the great carp like to hide. Once you get through this path you will eventually come across the Palace Grounds idol. Go into the building kill everything and go out the right door. If you turn around you will see another grapple point. Use this to get on top of the building and follow it to the back to see another grapple point on a tree. Follow this to another one on a building and hop down to the Feeding Grounds.

Now in this area you will see an old man and a bell. You don't need to talk to him but you can. All you need to do is ring the bell and feed the Great Carp the truly precious bait. After that is done just travel to the Guardian's Ape Watering Hole.

Once you are there all you need to do is just turn around and grab the whiskers for the achievement. If you want you can go back to the old man at the Feeding Grounds and give him the whiskers to completely finish the quest. Rest at the idol and go back to him where he passes to receive some carp scales.