Transfer some music into a playlist onto your Xbox 360 hard disk or a Xbox 360-formatted USB thumbdrive. An easy way to do so is to put in a music CD into your Xbox 360, and then record the songs from there.
With either of these connected, go to the "Customise FIFA" option on the menu, and then select "Customs Music and Chants". Choose the playlist that you've previously saved on those drives, and you're good to go.
Also, if you're using a Xbox 360 Slim that came with a 250GB hard drive, there's already a playlist named "Xbox 360 Custom Mix 1" pre-saved into the drive. You can use this playlist and the achievement will unlock. This handy playlist has helped me earned both custom music achievements in FIFA 11 and FIFA 12.