Meet the following conditions in Arcade Mode for hidden songs to appear. Play them once and they will be available in Free Mode.

Unlockable	How to unlock
All songs unlock	Play the game 50 times and all 3 songs will unlock.
gymnopedie (skip over MIX)	Get C or below on one song and A or above on another song (order doesn't matter).
Mighty Guy -Long Version-	Play "Mighty Guy" as your 2nd song and get an A or above on it.
TRUTH	Get an A on both your first and second song.