This is an achievement for the Cop Missions. I found this easiest on "Leadfoot Lawman" in the first tier. You will need to play this race 7 times to get this achievement. I scraped the walls, nudged a car and even hit the wall pretty good but didn't spin out completely on the next to last run. The description says "colliding" so I am really sure that means no head-on or rear end collisions with traffic. Swiping against stuff should be pretty safe.
Note: to get 3 stars on this mission, have at least the Dodge Viper from level 8 or the Porsche from level 9. (The Porsche handles better)