This definitely took a few tries for me. As with the other two time-restraint achievements, using power throws is the way to quickly bring down your opponents' health and win. Instead of getting somewhere between 1-8 damage for a regular throw, I was getting 16-18 damage pretty consistently. Just get a running start while holding the ball (double tap left or right on the D-pad) and after a few steps, throw it. You'll know you've done it right when the ball flashes and there's a sound cue, and when playing as Steve for this achievement, the ball will curve upwards into the sky after hitting an opponent.
Another important thing to note is that whoever is blinking is the current ball-holder's target, so if you're blinking, get ready to catch. Other than that, enjoy the nostalgia!