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