Outfits are unlocked by earning stars. A silver star (400,000 points) will unlock one outfit and a gold star (600,000 points) will unlock 2 outfits. Even though music videos don't have stars, they'll still unlock 2 outfits for every good completed one!
This achievement glitched for me (along with How Do I Look?). If that happens to you, you'll have to start over from the beginning! The achievement unlocked for me after collecting the last leg outfit item. It unlocked even though other clothing items on that save where still locked! I guess it just looks whether the other outfit achievements are unlocked or not.