This achievement is incredibly straight forward to unlock. Boot up your copy of either
https://www.trueachievements.com/Lips-xbox-360.htm,
Number One Hits,
Party Classics or
I Love The 80's. Once you've booted the game up and the game has finished connecting to the servers just scroll through the menu and press "A" on the page called;
My Lips. Once you do that the achievement will unlock.
This can be seen in the below video.
* Credit to 360GuidesAU for the video