You will first gain access to the Monster Truck in the level "The Mighty Foot". It's an unmissable vehicle as you HAVE to drive it to progress in the level, to kill 15 enemies with it, just simply run them over, the monster truck is pretty overpowered so if you miss one, reversing into them will do fine.
If you run over ever alien you come across, you will easily pop this trophy just as you get to the highway you have to drive on.