There are 4 races in the Shiny Stone Cup. You don't have to place in first for this achievement to unlock. You don't even have to finish the race. You can set up a Grand Prix race and have each AI finish, and the achievement will still unlock. As long as you don't get squashed by any falling blocks during the course of the entire race, the achievement will unlock after the game has been completed.
This achievement can be completed with a second controller. Set up a Local Grand Prix race, have a second controller, and play through each race at your own pace. There will be no other players on the field besides you and your partner, so you can go as slow (or fast) as you wish. The achievement will unlock after the scores have been shown.