to get this achievement you need to smash 5 billboards, there are 120 billboards in paradise city that are red with the burnout paradise remastered logo on it.
don't bother with the other billboards advertising other products. you can look up the locations.
some good starting places is the bridge between harbor town and white mountain which should be on a ramp. the second is near to where you first start which is a nearby construction site with a ramp just a few seconds from the beach with the corkscrew ramp. you can find it in downtown paradise, just north from the junkyard you first start at.