Here is the full list of all 10 Kero Blaster achievements.
Complete Omake Mode.
Beat Omake Mode while wearing the jacket.
Beat Zangyou Mode without getting wiped out.
Complete Zangyou Mode.
Beat Zangyou Mode with 2 lives remaining.
Beat Zangyou Mode while wearing the jacket.
Beat the game without getting wiped out.
Beat Normal Mode.
Beat the game with 2 lives remaining.
Beat the game while wearing the jacket.