This can be done in normal Career, but it can be boosted much easier. From the main menu go to Multiplayer > Create Session. Set it to private. Invite a friend and start a rally event, doesn't matter where or how many events/stages.
Simply drive around carelessly, until one of you has a puncture. Stop, swap out the wheel with the spare one and complete the stage, while your friend purposely drives slowly. Reach the finish and the achievement will pop. Repeat for the other person.