The game shows promise, but please make the player's projectile attack instant, or at the very least, much faster. It's tedious having to wait on it to go from the gap in the bullets where you are, all the way to the enemies that shot them AND wait for it to come back, only to have to do that 3+ times for nearly every enemy after level 1. Even when you're right next to enemies and repeatedly clicking on them, it still takes them longer to die than normal bullet hells let you kill enemies on the opposite side of the screen from you (in fact, maybe you should lower enemy HP across the board as well). It's worse if you're trying to do combos, because then you ALSO have to spend time dragging the mouse around to connect each enemy (and in the right order sometimes), all while they're moving around and shooting at you, requiring you to stop aiming and move around tightly-woven projectiles as well.
You say you're not good at bullet hells, but your game's core aiming & combo mechanics demand more skill and multitasking than any bullet hell I've played, continue systems notwithstanding...so maybe just make the full game a normal SHMUP instead (á la Gradius, Hydorah, etc.), with normal-sized hitboxes and with the current level 3 difficulty being the final game's final level difficulty.
I also think it should be made clearer as to when invulnerable bosses can be hit. For the start of June's boss fight, my attacks kept making the "immune" sound effect, but I also couldn't interact with the unique flashing bullets in any way (they just hurt me like normal bullets). It wasn't until after my first game over when I tried attacking the boss again and was suddenly able to deal damage, and I'm still not sure what I was expected to do. Likewise, the stasis tank boss should have a clear visual to show that the laser only disables its shield instead of dealing damage itself like you'd expect, and only while the laser itself is active (though I think it'd be better to have the laser disable the shield permanently so the player doesn't have to hover around the top corner of the arena the whole time).
Oh, and you should have a warning for when enemies are going to come up from the bottom of the screen, since that rarely happens in vertical SHMUPs.
P.S. Will the composer put the soundtrack up for download anywhere?