This achievement, along with Victory Parade, "Stars and Stripes", Model Collector, and 18 Wheels is Not Enough, can all be quickly completed using the New Game + options on a new save file.
In the New Game + options, set the Truck Availability Rules to "All trucks available from start" and Truck Pricing Rules to "All trucks are free".
The new save will start you off in the garage in Black River, with just the starting Chevrolet CK1500 deployed. To quickly unlock all 5 achievements, use the Global Map to travel to Alaska, and then buy all of the base game trucks from the truck store, making sure to deploy the TUZ 420. Note that no DLC trucks (marked as such in the store) are not required for any of the achievements.