Trophy Shield/Oversized Sock/Massive Armband
You're going to pretty much want THF subjob for this part. If you don't have it I'd recommend leveling it or you'll end up wasting a lot of your own stones as well as RL time. I preferred MNK/THF as Counterstance with VV/RR/Mounted Champion never required any healing and killed stuff fast without requiring too much of my attention (this part is boring and tedious.) To prevent time wasted to constant job changing, I would go in and farm one of each item then use a Scroll of Warp and send them to myself through the delivery box and repeat. Just hoard a bunch of, maybe 30 of each, and you're done with this step.
For the 3 NMs, you should be on NIN/WAR. Don't waste your time with DNC subjob or whatever. Proccing the red !! is what's most important and you need to be able to do it most of the time you engage or you'll waste time. Also, get the Abyssite of Discernment before doing this. It's extremely helpful. If you discover that you are unable to proc red then deaggro it (don't waste your pop hoping for luck, deaggro takes like a minute.) I typically did them in the order of Adamastor > Pantagruel > Grandgousier although priority should be given to Adamastor and Pantagruel when it's night time as Grandgousier is easy to deaggro at any time. Also keep a Scroll of Reraise handy as it can be used with Mijin Gakure to provide another source of deaggro. Use Gnarled Horn/RR/Mounted Champion for this.
Adamastor
There isn't really much to worry about. He's easy. If you can't proc red, kite him with movement speed or use a Sprinter's Drink. You can probably conflux him too although I never needed to try.
Pantagruel
Take him out of the pop area because you don't want other stuff linking on. He gets ice spikes after every Ice Roar that will last until he uses Morbid Hack. Morbid Hack can take you down to less than 10 HP and will be readied exactly 60 seconds after Ice Roar was used. You can avoid it by kiting it, so start running away at the 50 second mark. You can proc while he has spikes up although be careful about doing this as the damage increases as his HP decreases (maybe around 130 when he's very low.) Make sure to use Yurin and Myoshu to speed things up (fewer Ice Roars.) Deaggroing is similar to Adamastor.
Grandgousier
Fight it in the corner of where it's popped and you shouldn't get any links. He gains shock spikes after using Thunder Roar although they are much less potent than Pantagruel's ice spikes. You can proc while he has them up although it's difficult because he constantly uses Catapult and the you might be stunned also. Catapult counts as a weaponskill so you have to wait for it to finish before using a weaponskill. Catapult also goes through Utsusemi and will randomly dispel one buff if it hits you. You should use a full evasion build for this reason as you can still evade it. It can do a lot of damage when he HP is lower (900+ sometimes, maybe be careful about using Berserk although I'm not sure if that affects it.) It will ready Trebuchet follow by Catapult 60 seconds after Thunder Roar which can also do considerable damage. You'll be fine with a good evasion and the Regen that Mounted Champion provides although you should always keep a few temp potions/elixers/etc. on you for when you have bad luck. Deaggroing it is easy. Just run away, he'll eventually fall behind you because of Catapult. You'll probably get some links that you can kill later after you've reaggroed him. Myoshu and Yurin are very helpful. I could take him to 32%~ on any Katana/Dagger proc before he would even use Thunder Roar once. I don't advise meleeing during the spikes when he's lower than 50% as chipping away at your own HP raises the risk of death with Catapult becoming stronger. There is hate reset on the target of Trebuchet, for anyone that might be duoing or whatever.
After killing the 3 NMs and using another Scroll of Warp, I would change to DNC subjob for Briareus.
Briareus
I used VV/RR/GH and a full Haste build with meat as his accuracy/evasion is poor. Every TP move can be stunned with Violent Flourish. I recommend trying to do so as it will save you time (no TP wasted with Curing Waltz.) Keep your HP above 1700 as Colossal Slam can kill you otherwise. If gets off an 1111 Mercurial Strike, you need to run immediately. Don't bother recasting Utsusemi, just run or you will die. It will use Colossal Slam three times before returning to normal, all of which you avoid by running. This will also give your Ni recast ample time if it's down. Cast it after the third out of ranged slam. Myoshu and Yurin will speed up this fight as well. Really though this fight is pretty easy for the most part, I'd say much less annoying than Grandgousier and Pantagruel. Each fight took me around 7~8 minutes.
Alternatively, and perhaps ideally, you could use THF subjob and replace VV with MC. It may increase your helm drop rate and you can always use MC to restore your HP after every TP move (turn around if you have to.) I'm not sure by how much this could extend the fight, although in retrospect it seems worthwhile as the overwhelming majority of the time is spent gathering Briareus pop sets anyways. Maybe someone can try it and provide some feedback.
Sobek
I don't really feel the need to go over the NMs for getting Sobek pop set, they're all pretty easy. Farming pop sets can be done solo with GH/RR/MC although I think going in as a pair and putting a set on both and then just doing Sobek was better as we could farm time while we were in there very efficiently. I mostly duo'd this with my friend Lazytaru on NIN/WAR (VV/RR/GH) and BLM/WHM(ideally MM/Beyond/Ultimate.) Pull it out of the aggro area. It will cast a ga spell at some point along the way, the BLM should be ready to stun this if it's Blizzaga IV. Only stun Blizzaga IV through this fight as the time between its casts is shorter after other spells and it may otherwise begin casting Blizzaga IV when your stun timer is still down. Awful Eye gives hate reset and petrify so the BLM needs to be fast with Stona. You can proc grellow during the early stages of the fight although the BLM should be using crappy gear as you don't want him to have much hate. When its HP hits 35%, the NIN can start kiting it around, sorta. Just around in casting range of the BLM. The BLM can start going all out at this point with Blizzard V and the like as you don't want it building lots of TP at this point (Tyrant Tusk has a good chance of death at this point.) The heavy nukes will trigger its TP moves and you'll run out of range of Tyrant Tusk. Enmity Douse can be used. 5000+ Blizzard Vs will kill it pretty fast. We tried other things with Atma of the Einherjar for Resist Death and such, but I found this way to be the most efficient. You might die once in a while due to bad luck if you duo, but it's unlikely and not much of a loss anyways.