I'm not a shmup pro, just an amateur player, but here's what I think:
- Presentation is obviously excellent, one of the most beautiful indie games I've ever seen.
- Overall movement, collisions and controls feel really strong.
- Bullets are clearly visible.
- As some other users have stated, the chaining system is too forgiving right now.
- Rank system works fine, as far as I can tell. On my second playthrough I got hit more times, but also received more health bonuses, and the boss patterns were much more intense.
- I'd like to have an alternate slow-mode control scheme, Cave-style, where the ship moves fast while tapping the fire button and slow while holding it down. I think it's more conventional for shmups to be this way. Four buttons is a lot, and to reduce the number of buttons used is always a good thing. Also, holding or tapping Shift key activates Sticky Keys Mode in Windows, which is annoying.
- If you're planning to use this boss fight as a Stage 1 boss, then I think it lasts too long. First stages in shmups tend to be fast and short in general, because of their introductory nature. Judging by the length of a boss fight, it seems to me more like Stage 3 boss or so.
Overall, great job! I will keep a close eye on this project's development.
Of course, don't take my comments as something decisive. You know what to do much better than me.
Good luck!