Unless you specifically need to unlock just this achievement, don't try to grind it out. You have to finish 50 episodes of the game show for another achievement anyways, and each episode has a game of Bop It! included.
As far as expediency, losing Bop It! is always the way to go. If you do absolutely nothing, each round will finish in 20-30 seconds, and you'll only have to play two rounds to finish the game.