Here is the full list of all 40 Polygoneer achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Get 50k points on the level 5
Get a 5x combo on the level 5
Get a 3x combo on the level 5
Get 50k points on the level 4
Get a 5x combo on the level 4
Get a 3x combo on the level 4
Get 50k points on the level 3
Get 100k points in any level
Get a 10x combo in any level
Get a 5x combo on the level 3
Get a 3x combo on the level 3
Get a 5x combo on the level 2
Get a 3x combo on the level 2
Get a 7x combo in any level
Get a 5x combo on the level 1
Get a 3x combo on the level 1
Survive 60 seconds on the level 3
Survive 60 seconds on the level 2
Survive 30 seconds on the level 5
Survive 15 seconds on the level 5
Survive 30 seconds on the level 4
Unlock the level 5
Survive 15 seconds on the level 4
Survive 30 seconds on the level 3
Unlock the level 4
Survive 15 seconds on the level 3
Survive 30 seconds on the level 2
Unlock the level 3
Survive 15 seconds on the level 2
Survive 70 seconds in any level
Survive 60 seconds on the level 1
Survive 30 seconds on the level 1
Unlock the level 2
Survive 15 seconds on the level 1
Get 50k points on the level 1
Get 50k points on the level 2
Survive 60 seconds on the level 4
Survive 60 seconds on the level 5
Survive 100 seconds in any level
Unlock the bonus "hell" level