Here is the full list of all 16 Toybox Turbos achievements. It takes around 2-3 hours to unlock all of the achievements on Windows.
Earned 1,000,000 coins
Played a local match with more than 1 player
Achieved a 3 star rating for every event in the game
Collected all vehicles
Played an online match against any opponents
Beat all boss battles
Completed an event on every track in single player
Achieved 3 stars in an Escape event
Achieved 3 stars in a Countdown event
Repainted any vehicle with a custom colour
Unlocked a new cup
Achieved a 3 star rating for every event in a single cup
Achieved 3 stars in an Overtake event
Achieved 3 stars in a Time Trial event
Purchased any vehicle
Achieved 3 stars in a Classic race