Damn that's good. I made one attempt and it ended in Siege 1. I assume you did any%... what were your preferred weapons?
You're right, that first arena in Belly of the Beast is pretty crazy. How do you play it? I've been starting up the left side and working clockwise but those nightmare imps by the armored manc are such a pain. And then the cosmic baron always catches me off guard.
Nearly every weapon in the game is really good overall, but I would say my top choices are the Impaler and Chainshot, with the Cycler and Ravager coming out when I feel I need a higher rate of fire.
The Impaler is tremendously good, and should be the first weapon you try and upgrade to the 2nd tier (i.e. the 'Ruby' tier) IMO. When you upgrade it to that tier, you get two choices: Power up your bolts every time you use your shield in some way, or slow down time when you hold the fire button. The slow-mo upgrade is utterly worthless, so forget that shit. What you want is the power-up. As soon as you get that, you basically start launching supercharged bolts of doom. These things are so stupidly powerful, they literally one-shot Nightmare Imps and Hell Knights (if you headshot them) and can even superheat armor fairly quickly.
The Chainshot is almost as good, but falls a bit short for a few reasons. The main thing it's stupidly good at doing is pulverizing armor. Once you upgrade it, a single fully-charged shot can shatter an Armored Arachnotron in just a single hit, for example, which is insane. Sure, the SSG can crush armor as well... but can it do so from like 30+ yards away? Didn't think so! Its shortcomings are that it doesn't self-regenerate ammo like the Impaler (something I forgot to mention; jesus, that gun is the gift that just keeps on giving), it doesn't have quite the same range, and its rate of fire also isn't quite as high. It's still a phenomenal gun overall, though.
I'm not as crazy about the Cycler or Ravager, although they are tremendously useful in certain situations--especially the latter, since it can provide a steady stream of health once you fully upgrade it. The main issue I have with them is they simply can't kill as quickly as the Impaler and Chainshot, and they're also nowhere near as good as shattering armor.
Surprisingly, I've gotten to where I literally never use either of the shotguns. The basic Combat Shotty can be useful for applying burn and regenerating a bit of armor, but the weapon-switching is so slow I'd rather not constantly cycle over to it to burn targets, then back to another weapon. It's just too risky, and often not worth the reward. The SSG is super powerful, but its range is shit which seriously limits it compared to the Impaler and Chainshot. I personally feel those two guns render it damned near obsolete. It's still great fun to use though, and utterly WRECKS nearly everything provided you can close the distance.
I also don't think I can emphasize enough just how important it is to max out your shield early. The very last upgrade, which greatly increases the duration of the Shield Saw stun, is a godsend! That's one of the most important moves/abilities in the game, and for it to lock down demons for such a long period of time is something that will singlehandedly save your ass and make fights far more manageable.
As for that first Belly of the Beast arena, what I like to do is quickly kill the Battle Knight that runs towards you at the start of the battle, then immediately head counter-clockwise and kill the acid-spewing Mancubus up top. There's a climbable wall just underneath where he's positioned, and so you can use that to get up there to him. You can use the Shield Saw to stun him in place as you climb up there (and even well afterwards), preventing him from immediately counter-attacking up close. Once he's dead, you then work your way down and demolish the Armored Arachno with your Chainshot, using your Shield Saw to lock down his buffed/possessed Nightmare Imp(s) so that they're effectively neutralized the entire time. As soon as the Armored Arachno goes down, a Caco spawns near the middle of the arena, and so you have to turn your attention to it otherwise it's going to catch you off guard.
I feel this strategy is easier overall, because afterwards you no longer have the Arachnotron and Mancubus constantly bombarding you from the high ground as you try and deal with all of the demons down below.
Once you work your way down to the Armored Mancubus and kill him as well as his possessed/buffed Revenant buddy, a Battle Knight will show up, and I'm pretty sure killing him is what causes the 'Baron/Acolyte' duo to spawn in. As soon as the Baron shows up, use your BFC to take it out of the fight instantly (there's a BFC bolt in that arena, near the bottom, and so you'd might as well fire a shot!). Finally, focus down the Acolyte with something like the Cycler or Ravager. Since the Acolyte is a 'Leader' variant (can't be Shield Saw'd) and also doesn't give you much to parry, I don't find the Impaler or Chainshot to be nearly as useful versus it.