This is similar to an achievement from DiRT Rally. To unlock this one, you need to finish a stage while one or more of the car's parts are badly damaged. In DiRT 4, "badly damaged" means that you need to see at least "Heavy Damage" in red next to a certain part of the car in the Service Area.
EDIT: It's possible that some subsystem of the car needs to get into the "Critical Damage" state instead of just the Heavy one, so if the achievement won't unlock after following this method, try again by trying to get a bit more damage in. Take care though as Critical Damage means that that part is very close to failing, which will obviously make you start the whole process again if it does fail. Critical Damage and Critical Ware seem to be different when it comes to this achievement.
To unlock this without overdoing it and wrecking the car, pick any car you like as long as it's not from the R2 class, since you will need a little bit of speed. Go to the tune menu and stiffen the Springs and Dampers to the maximum. Reduce the Ride Height to the minimum, for both axles.
Now go and complete a few stages in Michigan (if you've purchased it you can do it in Finland too which is faster), since it has a high average speed as a location in general and a whole bunch of bumps, dips and jumps. Going over those with that setup will put a lot of stress to the suspension and the bodywork. After a few stages (I recommend going for a total of 6 medium length stages, ~6km each), you should see that the suspension is in Heavy or Critical Wear state. If that happens, go into the next stage, go slowly so that you don't crash and have to retire and reach the finish. The achievement will pop then.