Here is the full list of all 26 The Perplexing Orb achievements.
Find all 4 different short cuts. (1-4, 1-13, 2-4, 5-4)
Complete the fourth Challenge Level.
Complete the third Challenge Level.
Complete the second Challenge Level.
Complete the first Challenge Level.
Complete all three original Bonus Levels. (Maze, PitterPot, Lights)
Complete the final level in World 7, the final World.
Complete all the levels in World 6.
Collect all artifacts and complete 6-3. (Tiled Paths)
Complete all the levels in World 5.
Complete all the levels in World 4.
Complete all the levels in World 3.
Collect all artifacts and complete 3-5. (Perpendicular Tiles)
Complete all the levels in World 2.
Knock the can off the stage in 2-3. (Shrinking Circles)
Collect all artifacts and complete 2-1. (Industrial Circle)
Complete all the levels in World 1.
Grab a heart pick up.
Grab a rocket power up.
Collect all artifacts and complete 1-8. (Cornered Way)
Collect a treasure chest.
Fall off a stage in the main story mode.
Find a short cut!
Clear the first stage in story mode.
Knock down a finish post.
Collect an artifact pick up.