Here is the full list of all 12 BEAT 'EM DOWN achievements.
Kill 500 enemies with the dispersion weapon
Kill 500 enemies with the Zig-Zag weapon
Kill 500 enemies with the bounce weapon
Complete a song
Complete the tutorial
Get a x500 beat combo
Unlock level 2
Unlock level 3
Unlock level 4
Unlock level 5
Collect two million points
Find the Easter Egg