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