This achievement might not unlock right away after beating the final boss, and the final boss cannot be challenged again once they have been defeated.
In that case, if the final boss has been defeated and the achievement is still missing you may need to create a second profile and buy the first new car under the new profile.
Credits for this solution to Surobyk ( seen in the comments to this steam guide here:
https://steamcommunity.com/sharedfiles/filedetails/?id=23421... )