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