Here is the full list of all 8 Barrage Musical ~ Basic Danmaku Tutorial ~ achievements.
Game launched
Beat Stage A-7
Beat Stage B-9
Defeat Lightsaber Fairy in A-7 before countdown ends
Beat B-9 without taking a hit
Beat B-9 without taking a hit and defeat Lightsaber Fairy before countdown ends
Beat B-3 by restreaming (keeping your position below the boss, losing 1 life or fewer)
Beat B-7 without taking a hit, while keeping your position below the boss