Dirt Rally

In all seriousness though, looking at this description of the achievement, it doesn't sound that hard, does it? Well... there are few reasons behind why this is actually more difficult than it sounds:
The cars are quite sturdy, unlike their tires. Even with the latest patch, the tires still like to pop quite easily if you put a bit more force into it, while everything else... doesn't really give much of the certain word. Exact opposite of the real life, but Codies acknowledged that the damage system is definitely not up to tasks, so there's at least that.

The achievement often will not show up when you finish the event when you have other events going on. And by other events, I mean full championships along with the small ones in the custom and online.

And finally the most important thing... no one really knows how badly the parts have to actually be damaged. Which means you'll be going very close to 0% to be sure and if some parts will reach that level then it's the end of the event. I don't think I have to remind that to get this achievement you need to finish it, right?

Now that you are armed with this knowledge, let's move on.

Before you even think about attempting, there are few things that you need to check:

Finish all the on-going championships and events, regardless of the discpline, aka rally, rallycross and pikes peak. You don't need to go to Master, just so that there isn't one that is in progress.

Make sure that you actually don't have the achievement by asking someone to check your profile page and the list of unlocked achievements.

The car you'll be using for this is turbocharged and front engined.

Again, check if there isn't any event in the progress. Even custom and online. When it comes to online, you just need to finish all the stages, so don't start the monthly before there are all stages available if you want to get this achievement.

IMPORTANT. Turn off your "I always have to win against AI" syndrome, since you won't be winning this event. Trust me.

With that out of the way, we can go about what is the best way to unlock this achievement. The theory is quite simple but execution can be atrocious. You need at least 3 parts to be as close to 0% as possible when finishing the event. There are two parts that can be reduced to 0% while still being able to drive. One is as some of you probably already figured out, Turbo, second is the Exhaust. Getting both of them to 0% will result in a loss of power, quite drastic for most cars but you can still crash fairly easily.

The third part is where the problem lies. There are few candidates for this, though I personally advise to go for more than just one. Namely engine, drivetrain and radiator. Once you damage radiator enough, you can then proceed to accurately wear down the engine. Drivetrain and radiator will be reduced along with the turbo and exhaust, so you're killing 4 birds with one... or two stones, depending on the approach and part of the track.

Here are some guidelines which will make it easier to get the necessary results:

For those that need Cpt. Obvious, do it in Custom Event.

Wales or Finland are the best for this, as the sheer amount of jumps and trees around you will greatly help in destroying the underside parts of the car. You also don't need to worry about going out of the bounds and retiring, like in Greece or Monte Carlo.

Group B Quattro S1 (aka Sport Rallye) is most likely the best car for doing this. Suspension doesn't work on it, so damage from jumps racks up enormously, while the mad I5 engine still has more oompf after losing both exhaust and turbo than the WRC spec cars. It is also the only Group B car that is front engined and turbocharged. And it being an old car, it's DiRTy cheap (pun intended) to repair it, which will help with surviving.

Stiffen the suspension fully and completely lower the car. This will further maximise the damage taken from jumps and generally everything else.

Don't make the event too long. You want to finish it after all. The best amount of stages would be 5 or 7, depending on the car naturally.

Aim for an odd number of stages, so you will always finish on a stage after the service station. This will allow you to be precise with repairing/damaging the parts a lot more.

Good rule of a thumb is to set the last stage to be short one. It will be easier to finish if your drivetrain is below 10% (that thing can reduce it's durability by 5% if you land in a wrong way, once... keep that in mind) while the distance will be more than enough to bake some sausages on the engine and grind that radiator to dust with the help of friendly squirrels and their mighty trees.

Don't be afraid to abuse the restart button, especially on the last stage. It won't take away the achievement while learning exactly how much you can push the car before the Matrix happens is more than crucial here.

Repair the parts to about 10% if they're below 5% or something along those lines. Exception are of course turbo and exhaust, which shouldn't be touched at all when it comes to repairs. Also repairing other parts you're not aiming for may prove helpful in destroying the already badly damaged parts. Don't ask me why or how, it just seems to work that way.

If you get a puncture and rip the tire off, it will wear down on the wheel a lot faster. I once got retired because the wheels went down to 0% from just driving without tires. So even though you want to destroy everything else as much as possible, try keeping the tires intact as much as possible. I know, it's impossible with the baloons we have but when you get more than a single tire off... finish the stage as soon as possible. Just to be on the safe side.

If you'll be doing it just as I proposed, we have those parts to deal with:

Engine
Turbo
Radiator
Exhaust
Drivetrain

To destroy those parts you need to jump and crash around as much as possible. Crashing with the front of the car and keeping the boost at full output (aka don't let the throttle on the jumps) will damage the turbo and engine while having hard landings will quickly get rid of that nasty exhaust and will degrade drivetrain. Both things will make radiator weep quite quickly though.

Once the radiator reaches the critical point (co-pilot will inform about lack of power, that's about 30% radiators durability then) you can start getting the engine just so-so. To do that stick the car at 1st or 2nd gear and keep the pedal to the metal... or key to the switch if you're keyboard user I suppose. You'll make the engine blow in a matter of minutes. Which is not the intent, so make sure you're at about 15% engine durability before the last stage (Cpt. Obvious - check repair screen in service station). If there's black smoke coming of the engine... you'd best start thinking about finishing the stage. Good thing about engine (at least in Quattro case) is that it's quite durable. So even if you're at 6% you can easily finish a full long stage... if you don't crash into a tree at full speed that is.

Quickly after the radiator shows critical, the exhaust should go with the "weight reduction bro" way and you'll be left with turbo barely holding to its life if you've been grilling some sausages on the engine. Either way, once exhaust and turbo will get to 0%, you just need to focus on maintaing the under 10% status on the rest of the aformentioned parts, which is the tricky part.

Drivetrain will be destroyed from basically any bouncing, radiator not as much unless we're talking Finland. In either case, both of those will be the biggest problems to keep at very low amounts. So it's in your best interest to make sure both of those parts are at around 10% durability when starting the last stage. A big discrepancy between the two will be very hard to close up, since they'll be draining down on durability together. Best way to preserve that low 10% state is to simply drive very slow. Make it a leisure drive while using 30% of the throttle, letting go off the throttle whenever you catch air (best to avoid that at all in that case).

If you want to do it with completely other parts... well, the main thing stands. Everything other than turbo and exhaust that will get to 0% will result in retirement from the event. So you want to grind those things through rolling, jumping hard and crashing into trees up till they are at about 10% of durability.

In any case, at the last stage you should have all the parts in the under 10% state which makes this your last stretch to unlock the achievement.