Forza Motorsport 4

ALL YOU NEED TO KNOW RIGHT HERE!!!!!
Allow me to elucidate on what I did for this cheevo.

Select PLAY CAREER>GO RACE>EVENT LIST>5 boxes from the right in the top row you will find European Autocross C-Class>the middle event is NURBURGRING SHORT CIRCUIT...this event has only 80 gates, none of them tight...it has a time limit of 3:08...
YOU DO NOT NEED TO BEAT THE TIME TO GAIN THE CHEEVO!!!
YOU DO NOT NEED TO DO IT IN A C-CLASS CAR!!!
YOU CAN USE REWIND!!!
I used an F-Class Vauxhall Agila for some of the races. This is a tiny little sucker. Even my worst time in the Vauxhall was 3:19. A small E, D or C-Class will work or upgrade the Vauxhall if you're in a hurry.
Use one of the 2 rear views to clearly see where you are and take your time.
POP.
Update 2017!!!!! There are a few other cars choices that work in the Comments section.

Just go slowly through 10 Autocross events. You'll probably see the ghost car get ahead of you quickly, but they will generally have penalty times. Slow and steady wins this race.

Using Y to rewind if you hit a cone is okay.

You can do a track more than once. You don't need to do all ten different tracks.

You can do this in Online or Offline events (thanks peacemak3r).

You can do this in Rivals mode as well (thanks Spilner).

Both HAMbidextrous1 and DaGroovyGorilla's solutions are great.

10 autocross events is pretty simple :)

What I Would recommend is doing is.

European Autocross C Class (3 events)
European Autocross B Class (3 events)
European Autocross A class (4 events)

This will net you the Achievement and work towards the Factory Driver Achievement and the bucket list Achievement.

It's okay to take your time. No need to try to fly through as this will only increase your chance of clocking a cone and having to rewind (YES YOU CAN REWIND ITS OKAY)

I would turn off suggested driving and put your damage to limited (this increases your credits which in turn if you don't have the Ferrari collector Achievement this will help.)

Hope this helps!

Its a pretty straight forward achievement to get here's what I did: I did the first three classes (C,B, and A) these classes combine have a total of ten tracks to do this on. I used the VW Rabbit GTI since its a very compact car that you can go slow pretty easily and I just upgraded its car class as it was needed. The key is to go slow, use rewind if you need to, since it wont count as a miss. Take advantage of coasting whenever possible to avoid the need to brake a lot and to keep a steady pace.