This is more or less down to luck, though there are ways to make it happen quicker. If you drift long enough to activate a level 3 turbo boost, ramming an opponent while boosting will knock them pretty far. This is even more powerful if you use a big character like, well, Big The Cat. Eventually you’ll manage to knock someone off the course, and the achievement will unlock. I got this one without even trying for it, you’re very likely to get it by accident too just by playing through the game and going for the other achievements.