The Arena Master is no pushover, especially because of his cohorts (HMP gives him unlimited Sergeants and UV ups it to Captains, ugh). Normally I would suggest liberal use of the rocket launcher, but this is (of course) a shotty run. In such a case, I recommend clearing out the top or bottom side of the building you start in (if you can, kill the Cacodemons toward the right side to prevent respawn), then corner-shooting toward the left side. When you start to hear his scream, just keep shooting and he'll go down (eventually). If he tries to get close, there's a good chance the lava will prevent him from reaching you.
You can also try the berserk method, but that's a lot harder with shotguns due to knockback. You could TRY to knock him toward the boundary of the level and then keep 'im here until he's dead, but that's just a creative thought. I noticed you hadn't taken any packs or the chainsaw: if you're going to fight him in a line-of-sight confrontation, definitely use them to lessen the damage.