Quick description; I took photos of 200+ cars in under 45 minutes (Xbox One X + external SSD so mileage may differ).
Select any Drag Race and choose "Change Car". Using X you can sort on Car Type. Scroll all the way left to the first Car Type and choose the lowest level car like D, C or B if possible. Now start the Drag Race and if everything works, you will be matched with 4 to 8 different cars from this particular Car Type.
Once the race starts, hold UP on the D-pad for about 0.5s, move the camera back a bit (showing all cars in one shot) and press the right BUMPER/SHOULDER on your controller. It will quickly take a picture (not saving / editing / focusing as usual), tally all unique cars in the photo. Press B a few times and immediately Quit the Drag Race.
Now for the rinse & repeat; select the same Race, choose Change Car and select the NEXT Car Type. In some cases you can't easily change within the previously selected Car Type. By the time you done all Car Types (from left to right), you should have 160 to 220 photos already. If you are under 200, start from the left of the Car Types again and now select the highest possible car like X or S2. It matches you with different / unique cars for you photos.
As posted in the news section, this achievement will not pop or go live before Thursday June 18 and one should have/get an update for the game in the process.