Great work! the game's design is pretty solid for a jam!
Nice work on the sprites and particles!
Some things I would polish in a bigger version:
Pause gameplay during the upgrade UI
The blue and the red dragons did not seem all that different from each other.. maybe some type of build up animation for the faster shooting dragon would help.
The player controls felt a little clunky, like you release the key and the player still moves for a few hundred milliseconds. then this is exacerbated when you upgrade the players speed. I would set the players input methods to be in Update() and then adjust the player's ridged body physics in the FixedUpdate(). Here is more info on that via Unity Answers
I couldn't tell right away that I was fighting a boss until I noticed it had two heads. Im not sure how to announce it better... maybe a big health bare appears at the top or bottom? maybe it flashes when you hit it? maybe the background flashes when it enters? all kinds of options.
I think I beat the boss... or did I die at the last second?... I'm not sure because it just says thanks for playing... your welcome, for sure! but reward the player if they won. players like being told how great they are lol... and if I lost you could probably just restart the game and I would figure it out, but an explosion first is always best.
Overall a really great jam entry! I think you did a good job of ramping up the intensity smoothly and comfortably, while still keeping it challenging.. that's always a difficult balance, so big kudos!
Keep it up!!