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