Here is the full list of all 34 Spherical alliance achievements.
Master World 1
Master World 2
Tutorial Done
Master World 3
Master World 4
Master World 5
Master World 6
All Bonus Levels Unlocked
Perfect Tutorial
Perfect World 1
Perfect World 2
Perfect World 3
Perfect World 4
Perfect World 5
Perfect World 6
Perfect Bonus World
CoOp: Master World 1
CoOp: Master World 2
CoOp: Master World 3
CoOp: Master World 4
CoOp: Master World 5
CoOp: Perfect World 1
CoOp: Perfect World 2
CoOp: Perfect World 3
CoOp: Perfect World 4
CoOp: Perfect World 5
Find Hidden Bonus Level Gem
Find a Hiden Item
Find a Hidden Fire Shot
Unlock a Bonus Level
Fill a Level with Blocks