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.
Destroy 50 cars
Ride all the cars
Win a race in the Island Rally
Race in the Island Rally
Buy a Smasher
Buy a Conqueror
Buy a BullyBoy
Destroy 20 cars
Upgrade one car totally
Finish last
Destroy 10 cars
Win a race in the Construction Site
Race in the Construction Site
Win a race in the Desert
Finish first
Use log
Hit with missile
Race in the Desert
Upgrade the armor
Upgrade the controls
Upgrade the speed
To be destroyed
Use mine
Hit with machine-gun fire