Sorry for the wall of text.
For the positives: I think you have a great basic gameplay and aesthetic to build from, and I really enjoyed the music, especially how sections faded in and out in response to oncoming waves of enemies.
For some more nitpicky critiques: I didn't like the control scheme. I usually find games use Z and X instead of Q and W, with the up arrow also being able to jump. There was also one screen where you had to jump across a set of platforms while being shot at by ...lightning? (even though it looked like fire underneath?). I felt that was bit too much: it was the first platforming section, but we also had to deal with the parry that we just learned about, so it was pretty overloading. And the screenshake got a bit intense at times, especially when attacking / being attacked by more than one enemy at a time. I'd suggest toning it down a bit, plus adding an option to eliminate it altogether as an accessibility feature.
I think your game falls into the same traps that a lot of game jam games do: a really good core gameplay, but a way too intense difficulty curve with an overemphasis on the gimmick - in this case, having to rely on the parry far too quickly and too heavily. I've always felt the best way to introduce a complicated mechanic like that is "this is how it's done, it'll make your life easier, but it won't be mandatory outside of very specific situations for a few hours". With such a short development time, that few hours became 20 minutes and I just could not get into the groove of the game.
I think Stellar Sky Games had a lot of good ideas, like delaying when the attack registers to allow the player to parry ON the beat instead of just before, and including an assist mode was a good idea, and that the hi-hats were too prominent, and the waves were inconsistent in their length, and when multiple projectiles came at you you could only parry one of them and get hit by the rest.
For reference, I gave up on the sniper boss fight. I was going to quit in the first phase, but I found the assist options, gave myself more health and a longer parry time, but gave up on the second phase.
I guess I just didn't have enough of an investment in the game to really keep going. There was no story, no intrigue, no interesting visuals or set pieces to entice me to continue on, just the gameplay, which was good in short intervals but not enough to sustain me. I think some more obvious narrative elements, whether that means abstract imagery (if we have a visual reference, we can more easily see our progress) or a persistent voiceover (have you played Bastion? Because I think that kind of narrator would fit the gameplay well.) If it's more symbolic, then maybe the vertical falling and horizontal running sections could have some kind of deeper meaning? Falling into a pit of despair versus running from your problems? I dunno... You could also pad out the game with more platforming sections to get the player more acclimatized to your game.
You mentioned it being difficult to tell which 'weapon' to use. I think that could be done in a few different ways: enemies weak to the sword are small and have squishy, organic shapes, while bigger and more inorganic enemies need to be parried. You can also make the ghosts semi-transparent or dithered to show they're non-corporeal and you NEED to parry their attacks. Individual health bars could also show the relative damage of each attack, but that would probably distract from the visual design too much.
Hope all this useful, I'd be interested in seeing more of this game.