I know how it is to be a game dev on a deadline and have ideas of how to expand on a project, how it can be fixed or added to, etc. So please understand if I mention things you already want to fix or add.
1) There should be some transition between beating the boss and bringing up the upgrade system. Fanfare and text may be a lot to ask for, under jam conditions, but a lack of even a pause for the boss to disappear is a little jarring. Because the 'confirm' key is the same as the shoot key ingame, it's feasible a person could pick their upgrade unintentionally if they thought they were supposed to mash the key
1a) The upgrade system giving the player one of three choices, regardless of their performance in the fight, is a nice idea. Other games have shops during/between stages that require collecting coins, and they create a disparity between skilled players (who don't need the endless amount of upgrades they can afford) and beginner/unskilled players (who need support easing into learning the mechanics and can't afford it)
1b) I'm not sure what your sweet/candy-themed power up does because it uses the placeholder text descriptor
2) As above, the branching paths that let the player pick between a challenge for extra kudos or a straight heal is a nice idea, especially in that players aren't relegated to one or the other based on skill - cocky players can still attempt the challenge and get facerolled by it, but that they have the choice to do is the important thing
3) In many bullet hell titles the player moves at a normal speed when tapping/not using the fire button, and shifts to a lower speed when holding the button (often accompanied by a secondary attack pattern). "Focus" mode is an interesting take on the idea, allowing you slower speed and to see your hitbox as well, independent from firing your weapon. Since the nature of the genre is all about methodically weaving through curtains of fire, it's difficult to balance your player speed so that being in slow speed constantly isn't the dominant strategy, and I think there are enough bullet patterns of changing/static speed in your boss fights to warrant switching from regular mode to "Focus" mode
Overall I kept eating shit on the final boss but I had a fun time adapting to the fights. I'd like to see this game expanded with more bosses - maybe expand the number of challenges to pick from between each one, giving it a little Bishi Bashi/Wario Ware flavor of goals to accomplish. As far as sticking to the themes of the jam goes, I can see the 'cute' but I don't fully see where the 'timer' theme fits in beyond the stopclock in the top-right. I'm assuming that comes into play once you beat all the fights proper