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.
Achieved a 3 star rating for every event in the game
Collected all vehicles
Beat all boss battles
Earned 1,000,000 coins
Played an online match against any opponents
Completed an event on every track in single player
Achieved 3 stars in a Countdown event
Played a local match with more than 1 player
Achieved 3 stars in an Escape event
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
Repainted any vehicle with a custom colour
Achieved 3 stars in a Classic race