Here is the full list of all 18 PolyRace achievements.
Win the race of the day
Create 1 challenge
Finish time attack / easy race with no hit, no brake, boost always activated
Be in the top 10 in the race of the day
Be in the top 3 in the race of the day
Win 1 challenge
Win 10 challenges
Win 20 challenges
Win 50 challenges
Win 100 challenges
Create 10 challenges
Create 50 challenges
Create 100 challenges
Finish time attack / normal race with no hit, no brake, boost always activated
Finish time attack / hard race with no hit, no brake
Finish time attack / extreme race with no hit, no brake
Unlock all missions
Get 5 stars on all missions