Forza Horizon 2

Boosting:
I'm not sure if there is a way of boosting this, but this is the non-boost way how I got it this night.

Update from erod550:
Boosting seems impossible because you can only do Showdowns against other players. If you are offline the Showdown option will not be available. Also if you go to a Car Meet while in a private match it throws you in with the general public so as far as I can tell you cannot just do a Showdown against your friends to boost unless you get lucky on the matchmaking.

Intro / Prerequisites:
This is an online achievement. There's no option to start a showdown in single player. You can go for this achievement once you have access to all six car meets (which means having progressed far enough in the single player I guess).

How I did it / General strategy:
I'm not sure what triggers it, but after some time waiting at the car meet you can issue a challenge for a showdown via X button, or press X to join if someone else initiated it. If at least two players joined, a point to point race will start after the countdown.

Cars of any class can join, but lower classes get a head start of the higher classes. So for 5 out of the races, I used a A (800) 2011 Subaru WRX STI with Weight Reduction, Tires, Turbo and some other performance upgrades, so I focused mainly on handling.

Having a head start of the S1 or higher cars and a car that handles well (so no bigger crashes) the only competition I had was the other A and B class cars. The faster cars mainly could not use their high speed because of the track layouts. For one race (Nice) it took some tries, for the others it was quite easy. I would consider myself averagely skilled, so it's possible to win one race if you keep at it.

Saint Martin drag:
For the Saint-Martin race (a drag race) you need a fast (If possible X (999) or high S2) car with fast acceleration and top speed, and with my Henessy Venom GT it was possible after a few tries when I got a slower opponent. Your best bet would be a Maserati Tipo 61 (Barn Find), at least they have won every Saint-Martin race when one of those was involved (either fully upgraded or max S1 to try head start).
theMAYFLOWA pointed out that manual shifting helps to gain the few seconds you might need to win, so give it a try if you are losing to faster opponents.

Other tips:
- You can leave, wait 1-2 miinutes and rejoin the car meet to get some other opponents. This is interesting if either nobody joins the showdown or if someone you can't beat joins again and again.
- After winning one you can fast travel to the next one.

Quitters and disconnects:
- I thought winning against quitters counts as well. There was one race where an opponent left mid race and another where the opponent left when the race loaded and I ended up alone on the grid. I finished both and proceeded and the achievement popped. (I'm not 100% sure about this because I had one win before trying this but I think that was at a meet where I did not encounter a quitter.)
- Eurydace reported he finished against a quitter and did not receive credit.
- Lavindathar reported he got credit against a quitter.
- Getting disconnected after winning while waiting for the race to end does not count towards the achievement (thx CTM AudiRS6 for pointing this out)
It might be best to follow your progress percentage on the XBox One achievement app and check after these cases. Please report in the comments what you find out!

Hope this helps, if you have questions feel free to ask.

tl;dr: buy '69 Ford Mustang Boss or Ford F-100, upgrade to A, with AWD.

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As horstwayne said in his solution, apart from the Saint Martin showdown, it is best to take lower rated cars for this achievement, because you get a huge headstart if racing against higher tier cars. I stumpled upon two great class A car for this: the Ford F-100 and the Ford Mustang Boss.

The Ford F-100 is part of the free launch DLC and can be bought for 0 Credits after installing the free DLC. The stock car is in class D. What you want to do with it, is to search for a specific upgrade setting:

Class A
All-wheel drive
around 400 kW

or upgrade the car yourself with those specs. What you get is an absolute rocket for its class with decent handling as long as you use your breaks properly and don't break to late all the time. It is rather easy to beat cars without headstart while S and above cars won't get near you.

I got the achievement with the F-100 but others had more success using another really good car with supreme handling and good power, which is the '69 Ford Mustang Boss

I upgraded mine myself with AWD, weight reduction, better brakes and so on to 317 kW @ 1300kg. There are A Mustangs with much higher power available but I do not know how they drive. I uploaded my upgrade settings with the title "Showdown Mustang" under this gamertag "s3bb86".
I am no pro driver whatsoever, but it is possible for me to get several top 100 placements in class A rival events with my mustang.

edit 18. nov. '14: switched around some sentences for better readability.

With the except of the Saint Martin drag race (in which I used the 33 Stradale) I won every showdown the first time in an S2(998) Lamboghini Veneno. Even with head starts I was still able to catch up to any lower class cars. Use this car if you keep being overtaken by higher class cars if you're using the other methods.

In my opinion, at the moment this achievement in “enough boostable”, as there are few players active in car meets.

I won 2 races playing with a friend. We were in a private session, then we went to Saint Martin car meet. After waiting few seconds, we were in the same “lobby”. I started a head to head and, fortunately, only my friend accepted. He left me win the race and I got my first 16% of competition for this achievement. We did the same in Castelletto.
If you find another player active in the lobby, leave it and go to another car meet with your friend. Consider that I’ve lost a lot of time trying to do some head to head legit, as nobody else accepted my challenge.

However, I also won 4 races legit, with a Toyota Celica GT four RC ST185, pimped to class C (starting from D, paying more or less 20k cr). It’s a quiet 4WD, easy to control. When you find an active player accepting your head to head, usually he/she has a S1+ car, so you start the race a lot of time earlier than the opponent. You only have to drive through the finish line without crashing. Consider that I’m not a great racer, but with this method I won 4 races on 5 attempts.
The only race you can’t win legit with this method is Saint Martin, as X999 cars can catch up you in few seconds. In this case, you need to pimp a car and find a lobby versus a player with low class car.

I won this achievement yesterday 02/10/2016. If either yourself or a friend are in the car meet you can send a game invite, we were both in a game party together but doing our own thing not sure if this matters. Once they join and once the option is ready hit the x button for showdown and off you go. just repeat so the other player can win do this for all 6.

None of the other solutions mention any of this information so I felt compelled to have to write this.

There are a total of 6 car meets in the game. You unlock car meets after your championship win in Sisteron. Open up your world map, then press to change filter to display Car Meets only. Going from left-to-right, the car meets are:

Sisteron
Saint-Martin (drag)
Nice
San Giovanni
Castelletto
Montellino

If you have a boosting partner, one of you can show up to a Car Meet then send a game invite to the other person. I unlocked it this way with a random I met in free roam.