Hey General_Red, thanks for playing!
We clearly still need to do some work on communicating what the "spans" are. FYI every time you push the boss back past one of the arches it progresses to the next span. You'll see a banner drop from the top of the screen telling you which span you've reached (same time as your health gets recharged).
The goal is to push to the end of the bridge, at which point you'll win the game. Once you knock him down he's vulnerable so you can keep pushing him for a bit before he gets back up.
Also: You can perform a horizontal slash by pressing attach while holding your shield up, and then hold attack to spin your gun up quicker.