Chauffeur Service (20 G)
"Escort Heather Swanson to Arnett's apartment without damaging your vehicle."
This achievement begins immediately after visiting Mrs. Evestrom. Heather Swanson will show up, revealing she is Evestrom's daugher. You will then be tasked with driving to Arnett's apartment to further question him. You must do this without hitting any other cars, street lights, signs, etc... Tedious though it may be, slow and steady wins the race. Turning on your sirens will also help to keep cars out of your way. Continually check your map to make sure you aren't doing any unnecessary driving. The achievement will pop immediately following the cutscene after you arrive at Arnett's apartment complex.
A couple extra tips:
"Also to add there is no time limit.. so going slow and having your siren's on helps.." - Courtesy of Your Neighbors
"Just thought I would add that if you hit something but there is no cosmetic damage to your car, then you will still get this. I got it with hitting lamposts at slow speeds and a car hit me as soon as I left the drive way." - Courtesy of BENN1E