TL;DR: A build I was using before receiving the Bloodletter / Deathless combo that also worked without it in any form. Bolded stuff is barebones explanation.
This is what I am currently using to farm Mayhem III Slaughtershaft + anything else. I've been testing a lot of Legendaries and different effects, and with this I've been solid solo or in groups. Like many other Moze players, I was entranced by the Recurring Hex grenade mod, and its implications for Moze. I received it when I finished my OG Playthrough, and 100%'d the game in TVHM + Mayhem 1-3 with earlier experiments using it before the nerf.
The reason I chose Bottomless Mags is the shear value in the Recurring Hex crits that get generated. With this build you'll find great survivability, flexibility in gun usage with the ability and room to experiment, and a reliable way to clear Slaughtershaft and Proving Grounds with no real effort needed.
It's easily the most fun I've had in any game recently, and I haven't ran into many issues on MHIII because of it.
Essential: A grenade mod that generates vast amounts of critical hits. The perfect grenade is the Recurring Hex w/ Radiation, however I have seen other Grenades capable of the same thing. All that matters is that they're constantly critting.
There are two variants of this that I rely on. One is with Deathless / Bloodletter (you may not fully maximize the potential of this combo, but it doesn't matter. The survivability + retainable critical damage is wonderful).
The other is Megaton Mind Sweeper/ Atomic Boots / Breakout Suit. You'll FFYL every now and then with this one, but I managed MHIII Slaughterhouse with it all the same.
I use a varied amount of weapons, as none have proven essential compared to others. Currently I am using an Annexed Jericho, as the perpetual ammo regeneration allows me to constantly be landing immense damage with it. However, I generated the most DPS beforehand using an Anointed Corrosive Rocket Launcher purple drop. Remember, you don't have to rely entirely on Legendaries :D
Fighting Mobs will be where this build truly shines. Because of its flexibility in the guns you use, I recommend having a high mag high refund weapon like Lucian's Call for constant mass criticals and infinite ammo, and then two weapons slotted specifically for combatting larger bosses.
The only downside is that when something with a big enough hit box shows up, your grenades can't float crits like they usually do. In these cases I rely on my anti boss stuff. Whatever you're comfortable with.
Even with such a large amount of shields, I still have a careful playstyle. I try to keep myself on the outside of mobs and to collect them together for all of that juicy splash damage.
It's important that you're always mobile. Be jumping, sliding, and remembering the five D's of dodgeball. One of the advantages of this build is that you can run and gun at the same time, but always remember to be throwing grenades every second or more.
When you direct the focus of your Grenades + Weapon on a specific enemy, they melt quite quickly. Try and place yourself in angles where you can trigger a FFYL if you must.
Remember to use Iron Bear!
Yes, the damage is somewhat worthless, but Auto Bear can provide the cover you need to revive a downed ally! I use Target Softening when with a team because it increases damage from ALL sources, and Auto Bear also lands some hits with it. One important thing to note is that a great deal of Moze's best Anointed Triggers are on the end of an ability, so hopping out of Iron Bear gets yourself some juicy extras.
Always. Use. It. For as much as you're dodging and moving around, remember that it's a tool that we have infinite use of. There's no reason not to trigger extras.
If you read all that, thank you. Be prepared to lose friends over this build, as they'll either have their potatoes crashed or get unhappy with the efficiency of it.
Go nuts with it! I love the ability to just test out every Legendary without having to worry about it truly affecting my gameplay. Make it better, make it worse, share it! I know it's probably terrible, but I truly have no issues in MHIII because of it, so…cheers!