This time, Buck is not near where you are, but is north of Amanaki Outpost. That means you should fast travel there and then head north. Once you get there, it's time for yet another history lesson, and he'll tell you to jump in. Note that if you find the highest point of the cliff and jump in, you will get the Free Fall achievement/trophy.
Once you land in the water, find the piece of land with the vine that you can climb. Go through the door and you're now in a cave section. When you climb the next vine, you'll spot an enemy below you and if you have the Death From Above skill, then simply jump down and you'll kill him. For the next part, sneak up behind the guys and do Takedowns on them.
This will likely cause two Dogs to show up and sniff around. Either shoot them or knife them, and the drawbridge will drop and a Heavy Gunner will show up. If you have a Mine or C4, plant one on the path he will walk, or you could just shoot him in the head. In the next area will be 5 enemies, some of which are close together, so feel free to use Chain Takedown if you have it, or just shoot them all.
Go inside the little room and grab the armor on the crate if you don't have any, then use the zipline to get to the area below. You will likely be spotted in this area, as enemies can see and shoot at you from the gaps in the floor below you. Take care of the two guys on the same level as you, then start picking off the ones below you.
Once the coast is clear, drop down to the next platform, then use the zipline to get across. Follow the path, killing any remaining enemies, then use the next zipline to the following area. Drop down to the scaffolding and kill the two enemies that show up here, making sure you stay away from the acid. Keep going down and forward until you reach the entrance to a big area, but don't go into it yet (watch out for the blasts of hot water).
As you approach the big area, you will be able to see an enemy off in the distance, who has a RPG. Snipe him and the other two enemies, then go into the big area. Cross all of the rocks, keeping in mind to not hurry because of the hot water blasts, until you reach another big area. There are another three enemies off in the distance, so feel free to snipe them from here if you want. Follow the path until you climb the vine, then go up and kill the guy hiding in here, then open the marked door.
With the door open, you won't be fighting anymore pirates for now, so drop down into the nice, open cavern. With the bridge out, you'll need to find another way, so follow the path to the right, keeping in mind that the hot water boils onto the rocks below. Once you get to the vine, climb it, then the ropes, then go to the statue and hold the button to open up a secret set of stairs.
At the bottom of all the stairs is a Komodo Dragon, so kill it and you'll find another two at the very bottom. Go up to the coffin and grab the knife. As soon as you do, a booby trap will spring, with flames shooting out the sides, so sprint as fast as you can, then slide into the opening. As soon as you slide, move forward a bit and you'll have to alternate pressing a few buttons until you reach the clearing. With that, you'll be outside and the mission will be finished.
