Load up a quick stage in solo mode, choose any car but preferably a fast one (I used Puegeot).
In options, make sure under driver difficulty/assists to set vehicle damage to "affects handling".
The longer and more dangerous the map the better, I just used the default one though. Damage the car as much as possible, generally ramming the sides is good, and in particular head on collisions with either trees or the edges of railings/walls at high speeds will wear down the engine.
It might just be the engine that has to go, but most of my car was orange and it was roughly 2/3 to 3/4 of the way through the race when the engine blew and my car no longer moved (it had slowed considerably just before that). This is when the achievement popped.