There are 12 monkeys on the archipelago, and each one will give you a small quest to accomplish. You have to do all 12 of them. These aren't in order, but the challenges are:
1) Last Meal - Kill an emu or a deer and take the fresh meat. Cook it to make steak. Mix the steak with mushrooms to make steak and mushrooms and give that to him.
2) Golden Plant - Inside the safe room on the same island you get the quest on.
3) Monkey Bag - Get an animal skin by killing a deer. Mix it with a reel.
4) Find three exotic fruits - They're all over the place, you might even have them on you when you start the quest.
5) Cooked Special White Plant - The white plants are very common, just take one to a fire and cook it.
6) Lemonade - Mix a bottle of water and an exotic fruit together.
7) Green Beef Soda - Mix a bottle of water and a guarana plant together to make a drink, and then use a compressor on that.
8) Find the golden chalices - Again, they're scattered in that general area. Not terribly hard to find. If anyone remembers the exact locations, I'll edit them in.
9) Fish & Chips - Use the reel, a hardware kit, and the flexible branch (in that order) to make a fishing pole. Go fishing, dawn and dusk are the best times to catch something. Cook the fish. Mix the cooked fish with a cassava root.
10) Find the Santa Barbara statue - It's in one of the safe rooms on the same island that you get the quest on.
11) Find the four crab statues - They're all on the west side of the island, not too hard to find. See below for the exact locations.
12) Find the golden cat statue - It's inside a nearby chicken egg game (a tall, thin wooden box with a chicken on it) up a hill to the north.
--Crab Locations (thanks to Nikolai420)--
1. Behind the monkey on a ledge. You gotta burn/cut bushes to get down there.
2. Directly northwest of the monkey. It's on the same platform that the monkey is on.
3. There's a safe house not far from the monkey with a shed that has to be blown up.
4. Just northeast of the monkey is a few piranha. To the north of them is a campfire, wooden structure and gas tank. Behind the tank is a path follow this path to the final crab and an herb!
Thanks to MMMDI