DiRT 3

I just picked single race from the main menu then selected rally. I set it to Kenya - Crocodile Point then proceeded to race cleanly and drove carefully. After i finished it unlocked on the loading screen. I tried a clean race on a time trial but it didnt work. Make sure you pick one of the DLC cars.

Lancia Stratos (70s) or the Pugeot 205 T16 EVO 2 (Group B)for the rally event. I only listed the 2 above because they will be the only 2 selectable in this rally event. Just set it to 70s or Group B and select the car in that group.

This achievement requires you to complete a clean race with one of the cars from the pack, these cars are:
Lancia Stratos - 70s (Rally)
Peugeot 205 T16 Evo 2 - Group B (Rally/Rallycross)
Citroen C4 Rallycross - Rallycross
Ford Mustang GT - Trailblazer (Modern)
Saturn Sky - Gymkhana (This car doesnt count as its not available in a race)

You can unlock the achievement in the Dirt Tour, Singleplayer or Xbox Live Multiplayer (You cannot unlock this via a timetrial event)

The quickest way to do this is to start a Singleplayer Rallycross at Monaco - Casino Square, set it to 1 Lap and use the Citroen C4 Rallycross, seeing as you Do not need to win let the AI pass you at the start line and then take the course easy making sure not to touch any walls or opponents.

The achievement will pop at the loading screen after the race
Here's a video to demonstrate

Easy just go to single race choose rallycross and pick the Citroen C4 RallyX – Rallycross
on any track you like set to 1 lap then just dont crash go slow ( you dont have win this race!!) there you go you got it

( achievment should pop on loading screen)

EDIT: you can do this while in progress of The lively set achievment so you can do this faster than you think :D

Very easy get this achievement here is my way