Chimp
Make friends with the chimps on the island by talking to them and telling them jokes. If they are happy, they will give you gifts. At some point, one of them will deliver a banana leaf with piece of the treasure map inside.
Clam
Dive for clams on Airplane Island's West Beach; one of the clams will contain a piece of the map.
Crystal Island
A fragment of the treasure map is lying on the ground on Crystal Island. The island is hidden, and only revealed when the broken ceremonial forge on Volcano Island is repaired. Once revealed, Crystal Island can be accessed by swimming into the ocean from Airplane Island's West Beach.
Volcano Jungle
Explore the hot springs in the Volcano Jungle region of Volcano Island; a piece of the map can be found somewhere in the area.
Bottle
Pick up any bottles scattered along the beach and read the messages inside. One of the bottles will contain a treasure map piece.
Volcano
Climb to the top of the volcano on Volcano Island; a shred of the map is lying on the ground near the summit.
East River Plains
Enter the East River Plains through the Hidden Lagoon. Walk past the quicksand area and look behind the left pillar.
Cliff Dive
Head to the Tidal Pools on Volcano Island. Walk out on the platform and select "Perform Ceremonial Cliff Dive." Once the dive has been completed, you will receive half of a piece of the treasure map and a message that a shark ate the other half.
Tiger Shark
Drop a fishing line into the Tidal Pools. Eventually, the hungry shark will take the bait and the other half of the piece of the map will appear in your inventory.