Unlock the expansion and proceed to the world's Boss named Rampo. Proceed until you reach the last set of blasters, then drop down from the area and go to the other side of the 3x quills to find the secret pirate treasure.
Proceed to Gloomy Gem Grotto, on the right side of the lake. Follow the path until you reach the smiley platform. Then, use Flappy Flight to get some height and look for a platform on top of the rocks with the secret pirate treasure.
Use Flappy Flight to get directly above the Pumping Plant to find the secret pirate treasure on top.
Go to the entrance of the world, then look behind the tome to find the secret pirate treasure on top of a light. Use Flappy Flight to reach it.
Unlock the world's expansion and proceed to Velocity Terminal. After entering Velocity Terminal, go through the right entrance in the first sphere. Use Flappy Flight to float down to the far bottom-right sphere to find the secret pirate treasure on top of that sphere.