You unlock the cars by getting 100% in the storyline. This includes an unlock for the Ben Undercover car list. Ensure you complete the list before finishing the other cases or you might encounter a glitch stopping you unlocking the last car.
Here's the list of cars for you to cross out as you go:Police Cars
Semir 3.0 Police
Ben B32 PoliceSports Cars
Monster TruckAmerican Cobras
Hornet CopCobra Specials
Armored Money Truck
SOS 112Road Chiefs
Synetic ToursRace Cars
B32 Station Wagon
B32 Station Wagon Taxi
You need to complete a Single Race with each vehicle.
The best thing to do is combine this achievement with;
Use the faster cars to do all of the longer tracks, then when you just have cars left and no tracks, (there are more cars than tracks). Just use the 4x4 club circuit to finish all of the other cars.