Here is the full list of all 23 PolyBoost achievements.
Play the Tutorial
Collect 30 stars in Stage 1
The first 100 deaths
Finish all levels in stage 1
Finish all levels in stage 2
Finish all levels in stage 3
Finish all levels in stage 4
Finish all levels in stage 5
Collect all stars in stage 1
Collect all stars in stage 2
Collect all stars in stage 3
Collect all stars in stage 4
Collect all stars in stage 5
Collect all stars in all levels
Reach the goal in 1-1 in less than 2 seconds
Reach the goal in 1-2 in less than 2 seconds
Reach the goal in 1-3 in less than 3 seconds
Reach the goal in 1-5 in less than 4 seconds
Reach the goal in 1-6 in less than 3 seconds
Reach the goal in 1-15 in less than 8 seconds
Reach the goal in 1-18 in less than 2 seconds
Collect 60 Stars
Collect 150 Stars