I think it should be possible to do with your gear. I used an Epic earring as some compensation for the fact I use a Requiem Revolver, a High-Tech Ring, and that I didn’t have a set (i.e. your 3pc guild accessory set). My avatars/pet give about 10 pct crit and +2 dbr, but you have a Webley Mark for swapping, so I think it evens out.
Chain Snatch is a hugely valuable tool - it can cancel boss attacks, as well as determine when you’re able to hit an enemy. It is also the easiest skill to chain out of for cancelling purposes. Because the left side boss has so many I-frames, you would do well to throw out a Chain Snatch to test whether you can dump your cube skills. Watch my usage of Chain Snatch to stop the boss from spinning or swinging his axe. Are you making full usage of your cancels?
Left side will be harder because there’s more enemies. Here you need to learn the boss’s attack patterns: once you stop being able to hit him, he is about to jump and slash towards one edge of the screen. Right after he lands, he’ll send out a red wave thing. You generally cannot hit him until after he shoots the red wave. Right after he shoots the red wave, get behind him and Chain Snatch, and start DPSing until he does the next attack. If there’s a marked path on the ground after he lands, it means after the red wave, he’ll slash across to the other side. You can cancel the dash by Chain Snatching. I would try to make a video of the left side (because it’s generally harder) but I’m low on FP right now.
Edit: Chain Snatch also is an easy way to start off your combo because it inflicts bleed. You need to bleed your opponents or else you’re missing out on +26% skill damage from Saw Blade. For example, if you Death Hawk, Multi-Headshot or Moving Shot w/o starting off with some method of applying bleed (Chain Snatch, Kill Point, Gun Dance, 1a, 2a, etc), you’re doing ~20% less damage than if you had inflicted bleed.