For pushing outside of the arena, it was first boss. I never beat him. I did not notice a charge attack at all, he was always in melee range as I smacked at him. Sometimes he was a bit further away, but because I was pushed outside of the screen, my focus was on moving back into visibility, not watching the boss. His charge was not clearly telegraphed to me, but I don't play games like this very often so I might be missing common tropes and mechanics of this genre.
When I said charge attack, I meant that there are points in the game where the boss should move away and then run towards the player at a fast speed. What version of the game did you play? On desktop, browser minimized, or browser fullscreen. The player and boss should not be outside of the camera, and if they are this might be a resolution issue.