Alright, I started the game over, this time with the goal of making it to the final boss with Quiet Memory intact. On two particular attempts, I managed to do a couple rounds of Serenades and Shatter Stars before having to use the full heal. I then survived long enough for the boss to start casting spells. I took this as a sign to deflect them with Soul Mirror, which worked twice. But then the boss switched back to regular attacks, which targeted Sky 100% of the time. Even surviving several rounds after that, the boss still never died.
I'm curious how much health she has. The Quiet Dream seems 100% mandatory, and even then the fight is heavily RNG dependent. The only other healing item I imagine could help would be the rare berry, because every other item I found only heals about the same as the boss's attacks (who moves more often than you, even after the agility fruit). I definitely get the impression I'm missing something, so I'm open to hints.