This can be obtained by starting up a game on the new Classic Space Pack DLC.
Once you're in the game, turn on/plug in a second controller and hit on the second controller to set up a split screen game. Your "guest" will have access to everything your main account has. Assuming you have at least one instrument (your inventory will carry over from the base game, so you should have one), select it with both controllers and hold
with both controllers to jam out.
EDIT: Sabot Fox has pointed out that you will need two instruments, as both of your minifigs need to be playing a different instrument to pop the achievement.
Achievement unlocked!
