This method worked for 6 of the last cars I needed.
Go to extras,
Then Vehicle showroom
Go to a car you haven’t found yet
Then go to cases and go to Homicide free roam
The car you selected should be in the parking lot to your left (in front of the police station)
In my experience it worked for 2 door vehicles, 4 door vehicles and sports vehicles. but not service vehicles, it will also NOT work for customs.
I apologize if this doesn’t work for you, maybe it was just coincidence. Just thought I’d share since the achievement (without this method) is kind of random.
I also noticed that sometimes it may not spawn directly in the parking lot next to you but most of the time there will be someone driving the car in the area surrounding the lot.
I got my last 6 cars in about 15-20 minutes doing it this way.
Note: Some cars are said to only be found using certain desks. Most of the cars can be found using the "Homicide" desk but some of them people have had more luck using other desks, for example, the Chevrolet Tow Truck will be found using "Arson" and the Ford Convertible is found using "Vice".
This method was originally found by Epic Awesomeness from the X360A community. I have made changes to what he had written though, based off my findings, as well as comments below.