This can be done in a versus match with a second controller!
To get this achievement pick Green Arrow. You can get it by spamming B, but it doesn't make a lot of damage so maybe you won't get it in time.
There is a much easier way! When you hit 'down, down, B' Green Arrow sets 3 arrows on fire and this makes a lot more damage. Shoot the arrows with B, and repeat till you win the match. When your opponent is finished you should get the achievement.
Make sure you only shoot arrows and don't get another move, the achievement doesn't pop then