I liked the design of the map - The platforming parts were done well, the only thing that could be changed is making the "warning" signs a bit more visible. It wasn't exactly clear enough near that pit (around the middle of the map, maybe?) that I WASN'T supposed to jump down. The symbols blend a bit with the background, too. The "secrets" were perfect, it was a lot of fun to come back a bit to get a powerup that a while ago was inaccessible.
The enemy design... it was okay. Nothing exactly special, but nothing bad - in theory. In practice, the placement of the enemies was often plain annoying. At the beginning the horizontal shooters were basically "hit them once/twice then run to cover", since the gap between the missiles was rather tight. (the first shot only though, second was of course easy to not get hit by). The vertical shooters were a fun enemy, though rather harmless most of the time.
The 6-direction shooters though... they are technically a very-well designed enemy, though coloring them the same is confusing, given the player is unable to kill them (unless I'm stupid or something, in which case I'd like a clarification as to how to kill them). Their placement, on the other hand... was just horrible. They ended up being the most annoying enemy in the game... well, almost. They were placed too close to the edges of the walls. Their fire rate was way too fast to dodge properly in some situations, especially when their bullets were targetting a very important spot (like in the verical platforms moment for extra power-up). They ended up either making you cheese the section (the player can use the multijump to easily grab the powerup in the section mentioned a while ago, making the platforms pointless and confusing.), or were just not doing anything. Also, they don't seem to shoot when the player is below them?
Oh, and I also mentioned walls. The flying enemies can literally pass through them o.O
The boss... oh... oh, it was terrible, horrible. Even after getting to know its attacks, the indicators (if there even were any sometimes, I don't think anything tells you to stay away from the edges because the enemies will spawn?) are barely visible, the attack when it smacks with the hands was cetainly the most annoying. Also, more extremely tight gaps, with the jump that actually feels a bit weird for platforming... the controls weren't exactlly helpful either, it was sometimes easy to confuse the jump and shoot button during the "bullet hell" moments.
Oh, also, regarding the horizontal shooters - they shoot twice even if they die during their attack. WHY?!
The music was a very strong point of the game, it was very enjoyable. Although, after sitting in the menu while thinking about what to write, I noticed that the music fades out at the end, which is rather peculiar given it has to loop. Very small thing, but it's a pity it doesn't ACTUALLY loop well.
The art was great. Not really my style, but there's nothing bad I can say about it. The characters were looking really good. Also, really great background during the game, good work.
By the way, why not just give autofire to the player? (not sure if this was a power-up later on, or not, but it certainly wasn't there at the beginning.) It's a bit annoying to spam the fire button.
Also, the player moved slower when shooting, but even after they stop, there's still this short moment when the character is STILL moving slowly, which feels very weird.
Overall it's a good game, pretty enjoyable. It certainly can become a VERY solid, full version. Great work!