Start by pushing the boat into the water. Next, have all three characters jump in for the voyage to the island proper.
Once you reach the island, hop onto the upper ledge and make your way up the slope. Grab the straight pipe on the way. Make note of the pirate flag as well.
At the summit of the island is the Hermit's hut. Climb up to grab a Cave Painting. The cross pipe piece is here too - remember that. Finally, push the blue box over the edge.
Drop down and push the block to the right. Use it to get out of the pit. Keep heading right to other side of the island. Note the second pirate flag.
Move to the shore to find another box. Push it to the left to enter the caves below the island.
Place the straight pipe piece at the cave entrance, and then go back and grab the cross pipe piece.
With cross piece in hand, venture further into the cave. Pass the deflated hot air balloon, hop onto the upper platform, and hop onto the rope. From the rope, jump right to find the socket where the cross pipe piece goes.
Jump up and to the left from there to find a cave painting and an L-shaped pipe piece.
Grab the L-shaped pipe piece and head left from the rope. Hop up the platforms to find another Cave Painting.
Head down and left from the Cave Painting to find the socket for the L-shaped pipe piece.
Head right and descend the ladder. Head left and use the valve to fill the basin with water.
With this basin filled, you can start pushing the boat across the island. Push it into and across the basin, and keep going until you reach the second basin.
There is a ladder in the middle of the caves you haven't used yet. Climb down and head left to find some rubble, a pirate flag, and a bunch of TNT. Remember those pirate flags on top of the island? Have your other two party members pull and hold those, and then pull the one down here. That will open the gate to the TNT.
You'll have to use a chain reaction to destroy the rubble. Arrange the TNT barrels as shown above. You also should have noticed the bone near the first barrel when you started moving them. Pick up and hold on to that bone! You don't want to waste time coming back down here for it.
Pull the far right barrel back up the slope to the right. As you back into the heat chamber, the fuse will light. Push the barrel back toward the slope and let it roll down. It will roll toward the others, detonating them, destroying the rubble, and draining the basin the boat is currently sitting in.
Move around the island to get to said basin. Drop in and pull the lever to get the door out of the way Now start pushing!
Push the boat all the way onto the deflated hot air balloon. Have a party member turn and hold the nearby valve to generate steam, raising the balloon. There's also a Cave Painting under the balloon, but you'll have to force a respawn if you plan on jumping down to get it.
With the balloon and boat atop the island, push the boat down the slope. It will rocket forward, coming to rest in the water on the opposite side. Unfortunately, the Hermit hops right in.
Grab the box of crackers by the boat. The Hermit's parrot hangs out near the first pirate flag. Head there and use the box to lure him onto your shoulder. Now head up to the dog at the Hermit's hut.
Bring the bone up to the dog and taunt him with it. The parrot will record his bark.
Return to the boat with your new barking parrot. The sound will make the Hermit go back to his hut for his dog. While he's gone, have your party jump into the boat to sail out of this level.