Although this achievement appears to be broken for the EU release, this is unlockable for anyone with the NTSC version.
To unlock all songs: Complete quest mode. This means getting your 2nd silver trophy. See Solution for PARANOIA EVOLUTION in Dance Dance Revolution Universe
To play the songs: Enter Game Mode and play each song with a grade of D or better. If you have a turbo controller, turn turbo on for A, B, X, and Y. You will score 100% most of the time. You will pass every song. Alternatively - use whichever difficulty you are comfortable with and play - the controller is much easier than the dance mat... though the mat will certainly burn a few calories. That's not why you are playing this though.. is it?