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