This is definitely one of the easiest achievements in the game because you don't even have to do the first bop it action for it to count as a game played. With that said, start up a game of bop it and mess up on the first move. Do this 20 times and you'll unlock the achievement. Took me about 15 minutes to get all 20 done!
EDIT: According to hotdogmcgee, " If I did the first move correct and messed up the second move it ended every time. I was skipping the tutorial each time too, if that matters." So if for some reason this happens to you as well, just do the first action and then screw up on the second one. Rinse and repeat.