Make sure you have a smoke bomb in your inventory.
Head all the way to the SW edge of the island to Saruiwa. Climb the first tree stump grapple point and you should be in a small area with monkey statues. Before you squeeze through the rocks, look up to the left in this area for a climbing stump. Climb up here and work your way out to the first monkey statue, play the flute for him and you should see a small cutscene.
Climb back down and now squeeze through the rocks. Progress up a bit and you should see some cliffs/handholds ahead and on the right side of the path. Climb down to the second monkey statue and toss a smoke bomb for the second cutscene.
Return to the main path and continue onward. For the final monkey you will see another departure where you can climb down. Once you reach the water you will see the third monkey statue, which you need to bow to.
If you don't get the trophy, continue back up, climb to the mountain's peak, and complete the monkey sanctuary flute minigame.