In order to unlock this achievement, you must simply meet the requirements for the One Down, First Time, and Street Legal achievements. Once you have met the requirements for the first two, and then the third and final achievement from this lot, this achievement will unlock simultaneously with the third achievement. These three achievements do NOT have to be done in a specific order to unlock the Forza Triple Crown achievement, so tackle them in any order you would like.
I hope this solution helped! Leave a comment letting me know if there is any room for improvement! Thanks.