This is a pretty polished experience and a fairly challenging metroidvania. very impressive!
Story: I think I read in the comments/discord that you had a lot more story planned. What made it into the jam version seemed like a good start and while it wasn't a super deep story, rescue missions are always enjoyable.
Gameplay: I have mixed feelings on the controls. Neither KB+M nor the Controller options worked well for me. I am horrible at using WASD or arrow keys for platformers so I tried the controller. However I couldn't make left bumper for jump work for me very well either. I resorted to using AntiMicro to map the KB+M controls to different buttons on my controller(mainly mapping jump to A and mapping mouse moving to the right stick, which was clunky but worked). This allowed me to more naturally play. I think due to the way you need to aim the gun/sword you really should consider a button remapping system since I don't think a one-size-fits-most approach will work for this game.
That said, holy cow, the overall 'feel' is really great! especially the sword. You just feel so powerful and you can bounce around like crazy and it's really fun.
One issue I did have was that for some reason it took me 30+ minutes to finally find the final boss after getting all of the powerups. I don't know why I had such a tough time and finally had to resort to creating a paper map.
I thought the miniboss (to get the wall jump) was really tough and it took me several tries to win, but it was super satisfying when I finally beat it, so I'm not sure if I'd recommend changing much or not since I think having some hard challenges is fun. I think it just felt a bit stressful that I was forced to keep fighting the boss over and over till I killed it since I couldn't go back.
Also, I watched my brothers play and it looked like a few times they got to the mini-boss room with no mini-boss and were stuck till they restarted the game, so not sure if that's a bug or not.
Graphics: I thought the graphics were really good. Everything fit together really well and all of the extra fx (background parallax, chains moving, etc) were great touches.
Audio: this was my favorite part of the game. I think your sfx were perfect. Everything that needed sfx had it, and the quality was top-tier.
Enjoyment: I enjoyed beating the game and loved how powerful I felt with the sword. beating up on the enemies was fun and it was fun trying to learn to use the sword and gun to access different parts of the level to overcome the normal jumping limitations. For a one-month jam this game is seriously impressive.