A very interesting idea executed quite well, the hitbox being tied to a second form means you need to do additional routing and planning in order to maximize damage output, adding depth to the gameplay where it normally wouldn't be, and the lack of a homing shottype plays in this system's favour.
The music and artstyle are also great, both the art's pixel style and the music reminding me of Genesis-era songs complement each other nicely.
Aside from issues with the pause menu, my only real suggestion would be to consider the effect that the dual movement has on hitting single bosses more, as balancing between dodging and damaging when there's only one enemy on screen leads to not being able to hit them as often, and a result I found myself getting a time-out on Raiko's attacks more often than not (although this may just be a skill issue), although Benben and Yatsuhashi were both done well IMO.
In any case, thanks for the cool game, was a blast to play through and optimize for score :)