Here is the full list of all 12 The Impossible Game achievements.
Finish level 1 - Fire Aura
Reach 500 attempts without quitting
Jump 999x in total
Finish level 1 - Fire Aura without using any flags
Finish level 1 - Original Level without using any flags
Finish level 2 - Chaoz Fantasy without using any flags
Finish level 3 - Heaven without using any flags
Finish level 4 - Phazd without using any flags
Finish level 1 - Original Level
Finish level 2 - Chaoz Fantasy
Finish level 3 - Heaven
Finish level 4 - Phazd