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Strange, submitted this as cheats and got rejected. Oh well.
Secret Achievement: Pacifist - Let all of the SPACE INVADERS in stage Extra 20 survive. Secret Achievement: Invaded - Allow the final SPACE INVADER in Stage 0 to reach the bottom. Secret Achievement: Classic-UFO - Shoot down the UFO in Stage 0. Secret Achievement: Time Over - End a stage with a Time Over result. Secret Achievement: Unknown - Destroy Unknown in a Music Stage.
For the first one, though, it didn't unlock unless I let them all survive in stage extra 30.