OMG I figured out the battle mechanic!!! I tried what others said and I either did okay enough to pass through or failed so bad Tori yeeted me through the mirror. But clicking the first note BEFORE the second one would appear got me a flawless. You DO have to hit both notes, you just have to make sure you hit the first one before the second shows up.
Honestly it's just clicking the right note fast. You have to click the correct first note before the second one pops up whatsoever. Then click the correct one there. If the secondary one shows up before you click the first one, you missed the window to do so and it's missed and/or incorrect. Don't let the second note appear after the first without clicking the corresponding correct note to the first that appeared.
Helpful tip if using keyboard and mouse, move off the notes between clicking. I ended up messing one try up by a single note cause it thought I was still on the top row note instead of the second row note.