You don't need an upgraded car for this. I did it on my very first car.
This is actually a LOT easier than you think, and was 2nd achievement in the game. I wasn't even really trying for it, I was just going for as long a chain as I could.
On the east edge of the map, east of Bamburgh Castle on the sea, is a dune bike track. Lots of dunes, lots of jumps, lots of bushes and fences to crash into. Drive around there (not on the course, but across the dunes), and you won't be able to help getting a bunch of Air, Ultimate Wreckage, Drifts, Kangaroos, etc, to build up your chain.
It maxes out at a 5.0 multiplier (at least now, like I said I barely started the game), so hit 40,000 and stop. When the points register, the achievement will pop.
Don't need skill songs, don't need boosts, don't even need upgraded cars. All you need to be able to do is not flip your car over or hit anything in the parking lot on one edge of the map.