Here is the full list of all 15 Beatbuddy: Tale of the Guardians achievements.
Complete the game in under 3 hours
Complete level 6
Collect a total of 2000 Beatpoints
Complete level 5
Defeat 100 Soldiers
Complete level 4
Defeat the captured Parasites in level 4 without getting hit
Complete the Elite Training in the Camp
Destroy 200 containers
Accomplish 20 Rhythm Combo's
Jump through Snarestreams 100 times
Complete level 3
Complete level 2
Complete level 1
Unlock all the Extras