In the first chapter (which after several tries I managed to finish) the boss shouldn't be able to change direction when he's jumping to lounge at the player. Apparently onle when he does and he lands there comes a new crate to throw at him which makes the battle purely evading him instead of being active against him, which I found somewhat tedious.
When he starts the rotation attack it goes on for quite a while and he's not even slowed down a lot from doing the rotation, so keeping away from him is really difficult.
I would think he should stop the rotation attack (or continue rotating without pursuit of the player) once he had landed a hit.
For the second chapter I really quite didn't get how to avoid getting hammred. With a bit of luck -I managed to reflect a few of the missiles, but not for long...
Also, at least with my PC gamepad the button assignment isn't correct. the circle button is on the right which is correct, but the cross should be on the bottom but it's the top button (which would be triangle).