To earn this achievement, you must go through all of a specific difficulty (you have to beat Lou) as a lefty and righty. You do not have to start a new band to earn this achievement! Furthermore, you can turn off the game and come back to it later. Just make sure you're completing a difficulty that has 0 songs completed.
To turn on lefty flip, go to options, controller, and set lefty flip for player 1. Once you have done that, simply go into a band and complete a difficulty on lefty flip. The best choice is to use easy since you have to play the fewest amount of songs. If you're respectable on expert, I'd go use a mirror so that way you can earn more money for the $350k. Before using a mirror, I'd check if your television or monitor has a flip/mirror function. This should flip the screen and make it look like you're playing correctly.