You need the Batman 75th Anniversary for this achievement
After beating the stage normally, play it again on Free Play and choose Batman 1966, play the stage normally until you get to the dance puzzle where you gotta jump on the right colors in the right order on the dance floor, do it with Batman 1966 and the achievement is yours
To unlock Batman 1966, you need to beat the extra stage themed after the 1966 show, which you can only access after beating the story and going to a specific place in the Batcave