Keep In Mind that this is an achievement that is for 6 gamerscore. So if you want your gamerscore to end in 5 or 0 this might not be for you.
To get this achievement you have to go to "Careers" , then head over to "Championships". In the top left corner will be "Rally Open Championship" go there and choose "1960". First car will me a Mini Cooper S which is what you want to purchase, this will pop the achievement.
Once you purchase that car and pop the achievement press LB or RB to change Livery to pop up another achievement.