Here is the full list of all 24 Fury Race achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Ride all the cars
Destroy 50 cars
Buy a Conqueror
Destroy 20 cars
Destroy 10 cars
Buy a Smasher
Buy a BullyBoy
Finish last
Win a race in the Island Rally
Race in the Island Rally
Use log
Upgrade one car totally
Win a race in the Construction Site
Race in the Construction Site
Win a race in the Desert
Finish first
Race in the Desert
Upgrade the controls
Upgrade the armor
Upgrade the speed
To be destroyed
Hit with missile
Use mine
Hit with machine-gun fire