You'll be able to unlock the Jukebox by playing the game; by meeting certain conditions, you'll be able to unlock various musical themes in the game - some unique to the game, and others from other entries in the Pokemon Mystery Dungeon series.

Theme	How to unlock
Songs #001 - #131	Unlocked by progressing through the story
Songs #132 - #136	Unlocked at Normal Rank
Songs #137 - #139	Unlocked at Bronze Rank
Songs #140 - #143	Unlocked at Silver Rank
Songs #144 - #147	Unlocked at Gold Rank
Songs #148 - #152	Unlocked at Platinum Rank
Songs #153 - #156	Unlocked at Diamond Rank
Songs #157 - #160	Unlocked at Elite Rank
Songs #161 - #163	Unlocked at Ultra Rank
Songs #164 - #166	Unlocked at Hyper Rank
Songs #167 - #169	Unlocked at Master Rank
Songs #170 & #171	Unlocked at Grandmaster Rank