Finally beat it :)
Story: pretty basic but rescuing someone always feels satisfying after you had to work at it.
Gameplay: not too bad actually, but I was unable to play with a KB+Mouse. I had to use antimicro to map the controls to a controller (otherwise I could barely play since I'm so bad with KB+Mouse). My thoughts; sometimes it seemed like pressing Up (W) helped me jump higher. This wasn't noted in the pre-game instructions and I was never sure if maybe I was doing something else that was giving me a bit of extra 'oomph' for some jumps that I couldn't make from a standstill without pressing up/w. Double jump worked pretty well. Sophia told me there was a jetpack but I never found it (despite beating the game and finding Dad) so I wasn't able to test that. when fighting, sometimes my sprite would face the opposite direction after my first swing. I think this happened mainly after an abrupt stop (maybe?) but I wasn't able to reliably reproduce the issue. I learned that I needed to give myself more space when engaging in enemies to compensate. I've run into similar issues myself so it might just need some extra tuning.
I agree with the comment to consider ways to block/break bullets with an attack but this only came into play against the Double Jump boss and his floating buddy with homing gumballs. I seriously had a tough time with this guy and had to basically do laps, clockwise, around the level to lure to little guy up (so the top platform would block the gumballs) then when he got close, I could drop down and smack the Boss a couple times before doing another lap. I kept wanting to be able to get a few more attacks in but the homing missiles were too much for me to stand still for long. Maybe even just making the homing missiles breakable would be enough.
I also think you need some level-switch transitions and/or allow the player to use doors rather than making them insta-use. if they are instant use, definitely need a transition effect I think. either a screenwipe/fade or something. not a huge deal, but would smooth out the transitions. Ditto on the music transitions. either let the music keep playing, or fade out one track before fading the next track in.
Minor gripe that some level text was blocked by the hearts.
Minor gripe that I wasn't able to 'feel' getting hit. either with a graphic, or getting pushed a bit, or some other visual feedback (sfx feedback discussed in music section).
I liked the level design in general since it was simple enough that I could "almost" keep it in my head, but in the end I resorted to Old-School paper maps :) there's probably mixed opinion on that but I did enjoy trying to map out all of the connections, which helped me realize when I was backtracking into earlier sections (music helped here too!). I did like that the rooms connected so that you could backtrack a bit into earlier rooms, but it did seem like as soon as I got the Double Jump and Wall Jump that it was a little too obvious on where to go next, which made the game feel a bit more linear. But for a one-month jam that's a tough thing to balance. To me, it's obvious you were on the right track with the earlier parts of the game and I'm assuming you ran out of time to keep that approach more consistent for the later part.
Graphics: I think the graphics were pretty consistent and fun to look at. Your enemies and your player were the strongest. The level graphics were ok but there was a lot of variety.
Audio: I really loved the main track and I especially loved how the further you went, the track slowed down and changed up. It helped provide additional audio clues that I was progressing in the right direction. After getting the high-jump boots I managed to get back to an earlier room and the music sped up to the original song which kinda reminded me that maybe I'd been here. After consulting my paper map I found out that I was indeed in the older section and was able to quickly decide to go a different direction.
I really missed SFX though. as I said above, it was often tough to know when I got hit unless I saw the hearts actually disappear at the top of the screen. For a short game this wasn't too bad, but the lack of SFX was definitely noticed when juxtaposed with the really great soundtrack. In my experience I've found that a few SFX can make a huge difference so definitely something to add to your gamedev toolbox sooner rather than later.
Enjoyment: I enjoyed playing! the music really really helped and I'm still humming it in my head, and hearing the various variants was really fun too. I'm glad I was able to beat it and would definitely love to play an updated version if you decide to polish it up and submit to a SMVM in the future.