This is earned by falling off the edge with the same score as your best scored earned. Your best score will be shown on both the title and the end screens, so you just need to fall off the edge with the same score. This can be tricky, as stars give you 3 points for running over the tile in addition to any turning points you may gain, which can push you over your goal and increase your target score.
Because the difficulty increases the higher you get your Best score, I strongly recommend getting this out of the way early. The smaller your score, the less painful going over it by 1 or 2 will be.
If you are close to your best score (but still below it) and fall off, I can also confirm that using a Save-Me continue still allows you to earn this achievement. A continue costs 100 stars for the first one, and increases with each usage during the same run, so try to keep your best score low prior to obtaining this achievement so that you don't have to use continues.
Lastly, view the solutions for "Have You Lost It?", as it details a trick from Noodles Jr. involving the Windows key. Specifically, it forces a pause, and can cause you to not earn a point on the next turn. With careful usage, you can prevent a star from pushing you over your best. Additionally, these solutions give some additional tips on how to get to a specific score value, which is what you will be doing here.