Named after an early 90s Sega fighting game. This achievement is quite simple.
Do exactly what it says on the tin (i.e. don't use the A button to use an item for this)
Most people will get this without even trying (i.e. normal play through), but to make things easier use a Level 3 Drift Boost or a Dash Panel to hit someone off. The achievement should pop up.
It can be done within any mode with rival racers. (i.e. NOT Time Trial, or Battle race). CAN be done on Xbox Live apparently.
Will unlock immediately! Not at end of race.
I haven't personally checked if it can be unlocked in Xbox Live play.