I got this achievement my first time attempting it; the key is to quickly find an item box, and to fire an "aimed weapon" in an event. I surprisingly got this unlocked using a firework, but I assume either using a snowball or front-fired blowfish will work just as well. Take your time and shoot one of the forementioned items at an opponent.
If the first one fired doesn't hit an opponent, (you'll know, the game notifies you as to when you hit a target,) then pause the game by pressing "start" and restart the race.
If you do hit the target, hold back on using any other offensive items until after the race. The achievement will pop after the race ends, regardless of your placing.