Here is the full list of all 21 Lucky Burst achievements.
Unlock 2nd weapon
Die Once
Killed by the room
Kill 100 foes in arcade
Die 20 times in arcade
Die 100 times in arcade
beat any level on impossible
Beat any level on hard
Beat any level on normal
beat level 1
beat level 2
Beat level 3
Beat level 4
beat level 5
Beat level 6
Beat level 7
beat level 8
Beat level 9
Beat level 10
Achieve 1,000,000 kills in arcade
Achieve a high score of 300 in arcade