There is an even easier way...
Navigation to the challenge is as stated...
Select 'Play Career', 'Go Race', 'Rivals' and then the second tab called 'TopGear Rivals'.
Select the first challenge called 'A Reasonably Priced Car'
The easier way to get this achievement is to run the course slow speed to learn it the 1st time, then when you are done keep selecting "A" until you are back at the RIVAL board.
Press "Y" to CHANGE RIVAL and "A" to select your own gamer tag from the leaderboard. Then select "Set As Rival." Finally, go back in and run the race against your previous Ghost. Beat it and you get the achievement.
The 1st race will also get you the achievement for