When you complete the following tasks in Arcade Mode the corresponding hidden songs will appear. Play the song once for it to become available in Free mode. Play the game 50 times and ALL 3 songs will become available.
Unlock gymnopedie (skip over MIX): Get 'C' rank or below on one song and 'A' rank or above on another song (order doesn't matter).
Unlock Mighty Guy (Long Version): Play 'Mighty Guy' as your 2nd song and get an 'A' rank or above on it.
Unlock TRUTH: Get an 'A' rank on both your first and second song.