Here is the full list of all 25 Audio Arena achievements.
Use a shield to kill a dot worth 50 points or more
Kill 50 Red Dots in a row
Kill 1 dot worth 100 points
Finish a song killing only purple enemies
Kill 1 dot worth 50 points
Complete a level without killing a dot
Keep a mine alive for 15 seconds
Get a combo of 500 dots
Kill 10 dots using a shield
Get 150 points using the bomb
Kill 400 dots in 1 song
Get a combo of 250 dots
Kill 15 dots using missiles
Kill 1 dot worth 15 points
Kill 15 dots using an aimed missile
Complete the song without ever going out of sync.
Complete a song using only 10 powerups
Complete a song with maximum beat sync
Get 5 perfect beat syncs in a row
Get a combo of 100 dots
Complete a song
Last longer than a minute
Get maximum sync bonus
Complete a song with zero dots left alive
Get 400 points using 1 Bullet