He's a super-boss designed to be as cheese as possible; I'd recommend waiting until you're doing the Dark Cave sidequest before taking him on as you'll revisit Shinra HQ during it. He's been redesigned for 1.5 to be much more beatable when you return during the Midgar Raid but in 1.4 it'd be a much better idea to take him on after getting access to the Disc 3 stuff.
The first thing I'd say is to have 3x Protect Vests to halve the Shoot damage going out; the following attacks have the Shoot element:
-) Lapis Laser
-) Missile Array
-) Warning Shot
-) Tower Laser
-) Amethyst Laser (also Fire)
-) Coral Laser
The only other elements going out is Water from Submersion, Hit from Arm Attack, and Shout from Stern Warning. Shoot is the important one; it can also be blocked with Shield if you have it. In terms of statuses, guard against Death using either Deathforce or Destruct/Odin + Added Effect. The other statuses can be dealt with using Remedy/Esuna or Dispel.
In terms of team, I would recommend fielding Barret & Cait Sith for their naturally high defences and give them armour that props up their Magic Defence. If you can get Defence and Magic Defence past the 200 mark then it should greatly reduce incoming damage. They should both have Esuna+All, Dispel, Revive, and Restorative so they can keep the team ticking over and if one gets grabbed, the other is there to keep supporting. They'll need some kind of attacking option though in case your damage-dealer gets grabbed; Cover + 5x Counter Attack on Barret would be a good shout, and/or Cait Sith using Enemy Skill abilities.
About Grab; only one Arm is capable of using Arm Grab (the Right Arm); the Left Arm has had its AI disabled for this ability so once the Right Arm is killed you won't see Grab again.
Your third guy should probably be a caster. Vincent has higher physical defence than normal which should help, though Aeris could be brought in with something like Planet Protector/Pulse of Life as a panic button (though this will probably not fill again if Sadness is being used). They should be making use of W-Magic & MP Turbo (maybe with a summon like Bahamut-ZERO on Quadra as this circumvents the 1-use limit on Summons).
For logistics, you're going to need a lot of items. Turbo Ethers can be acquired from the North Crater by feeding Magic Pots Ethers (not Elixirs), and the bosses from Midgar Raid should provide a lot of money for stocking on things like Phoenix Downs, Remedy, etc.
In the fight itself, the Protect Vests should make the opening attack and Lapis much more survivable. He then alternates between Missile Array (his physical attack) and a 'special' like Submersion, Stern Warning, or Lapis Laser. When an arm is destroyed, his attacks will change.
Phase 1
-) Lapis Laser
-) Missile Array
-) Stern Warning (Shout: Confusion, Paralysis - single target)
-) Submersion (Water: Sleep, Silence, Darkness - single target)
Phase 2 (1 Arm Destroyed)
-) Amethyst Laser (Fire: dual-drain)
-) Tower Laser (single target)
-) Harsh Warning (Physical, non-elemental)
-) Stern Warning
Phase 3 (both Arms Destroyed)
-) Coral Laser (Instant KO, 60% chance)
-) Missile Array
-) Time Warning (Shout: Slow, Stop)
-) Submersion
Phase 4 (Core at 50% HP or lower)
-) Rainbow Laser (Reduces Defensive stats by 10%)
-) Tower Laser
-) Missile Array
-) Stern Warning
It's best to save all your burst damage for this last phase; Quadded Summons will be particularly good there. Rainbow Laser's effect will be removed if a character dies (like Hero Drink/Dragon Force effects) so it isn't a permanent defence loss. The last thing to mention is that he'll use a powerful attack when he dies; make sure to try and keep people topped up and have MBarrier active at all times in anticipation of it.
