Q:

How can I beat Hyperius the invincible? 

So two friends and I (2 sirens with Res, one gunzerker) have been trying to kill Hyperious for a couple hours.  At best we could get him down to about 1/4th health. 
We have The Bee and the Conference call and we know to res each other, we know to stay spread out, but his AOE "nuke" attack is so long range. 
We're thinking the trick must have to do with Aggression management and his robots.  Once you kill all 4 robots he's vulnerable, but still hard to kill and his aggro seems random; even with 2 Sirens we couldn't make sure everyone stayed alive.  It's not that we healed too slowly (our phaselock came active almost instantly) but at some point it'd always wind up that both Sirens were down, and if the Gunzerker tried to res one of us, half the time he got taken out too. 
Also, the Bee seems oddly useless against him.  I know the bee itself hasn't been nerfed, but the damage boost seems useless in this fight, even when the shield is up.  Is this due to the shields or some special property of the boss or what? 
So what do we do with his robots?  Leave one alive, shoot Hyperious when his shield is down, kill all the robots ASAP or what?  What team should I have?  Do we really need 4 Sirens with healing spec?  
How can we kill Hyperious? 

A:

The way I have beat him in co-op was with myself as Maya and my friend as Axton.  Axton used his turret with bubble shield at the start which blocks the first blasts fully and I was throwing the baby maker at hyperious with the bee equipped took him down to half health.  Then you just need to keep stopping his bots from connecting to him so he can't use the blast or have his shield, we both used conference calls for this save your SMG ammo until he hasn't got a shield.  
Try to get a relic to boost tediore dmg and try to keep the bots alive as long as possible but you will eventually have to kill them all.  When this happens Axton should throw down turrets to attract him (hopefully, worked for us) then throw your baby maker and you should have him dead.  By the time we killed all the bots he had less then a quarter of his health left so it wasn't too bad with him jumping around.  Dropped some bad loot though :(

A:

Assuming you don't have access to the Bee and/or Baby Maker, or do not want to use those combos:

Have a full group with a variety of characters and useful team bonuses whenever possible.   One of your members should be a Siren with a strong (Angelic) Nurse class mod that is going to be your primary healer, which should give everyone 220 to 240 health regen/sec.   Having Axton with Phalanx Shield Turrets is also highly recommended (Grit wouldn't be bad either, even if it only works against the Novas some of the time).   High-capacity shields with short recharge delays are also highly recommended on your non-healers... note that this excludes the Bee. 

Your healer is going to stand next to the pipe that is just to your left when you enter through the gate.   The job of the other players is to keep Hyperious and his minions pathed to the left of the pipe so they do not gain LOS (Line of Sight) on your healer.   This means trying to keep him away from where you entered, but not heading toward the back of the arena. 
Note that If you head too far back, the uneven landscape will prevent your healer from getting LOS for Res, and it is too far of a run to be safe for them to expose themselves.   In theory, a sniping Zer0 could hang back with your healer, but you're severely increasing the chances of Hyperious moving into LOS on your healer and ruining the strategy, and to keep both of them out of LOS would require getting Hyperious to track to a much more specific area. 

Pay attention to Hyperious' animation and audio cues.  He telegraphs his Nova attack with both, giving Axton time to throw down his shielded turret (barely), and giving your healer time to duck back behind the pipe which will block the Nova attacks. 

Immediately post-Novas, the healer should use Res on any distant party members that need to be raised while she or Axton (if he survived) work on saving any remaining downed party members. 

The healer needs to rush back to cover, and anyone needing health restored (hopefully not too much) quickly should move to the opposite side of the pipe where the gap allows the healer to shoot/heal them back to full health. 

Repeat this process doing as much damage as possible to Hyperious when he is exposed, including your healer who should be able to attack him between Novas rounds by stepping just outside of cover (but be careful of his minions while they are still up). 

Once Hyperious' minions are down... unload everything you have at him but your healer should not step out of cover anymore unless it is to Res, and should focus on keeping everyone's health up between Nova rounds which will come more frequently. 

Other Notes:

I have heard from others, but not verified myself, that Hyperious can be staggered when he is preparing his Nova attack, which prevents him from using the attack.   Sorry to say I don't know exactly how this functions, but it probably requires critting with a certain amount of damage.   This may be a way for Salvadore, Zer0, or Gaige to assist in an "offensive defense". 

Gaige has a potentially great build if you can get ahold of a level 50 Law (Pistol with bonus melee damage), level 50 Order (Roid Shield).   Combined, they give Gaige healing via melee attacks.  Have her use the Slayer of Terramorphus class mod (or whatever else allows her to max out Anarchy stacks at 600), and a relic that either raises maximum health or melee damage.   Spec her through the Anarchy tree all the way down to "With Claws" (which gives an Anarchy-based boost to melee damage [+360% at 600 Anarchy] and more melee healing) and get Discord along the way (reload early for healing... slowly consumes Anarchy), make sure to also take the "Cooking Up Trouble" skill which gives health regen as long as your magazine is full (since you won't really be shooting with Law it's a constant regen). 
If the party Siren is using Angelic Nurse class mod, Gaige will have access to thousands of health/sec healing while meleeing (but it will degrade over time as her Anarchy goes down).   She should begin the fight already charged with 600 stacks of Anarchy.   She should begin using melee attacks against Hyperious, which will eat one stack of her Anarchy per hit (but for huge damage), then when his shields go up, switch weapons to something with a small magazine to build Anarchy back (preferably something corrosive) against the minions.   Whenever Hyperious is going to use his Novas, fire Law once and reload to activate Dischord and start extra healing, after both Novas go off (assuming you survive), fire Law again and reload to deactive Dischord, and resume melee attacks to refill health. 

Admittedly, my Gaige is not ready for Hyperious yet, so I haven't proven this build against him... but on paper it certainly looks like if she can get her max HP high enough that she should be able to melee/heal through the Novas. 
Hope this helps! 

A:

So, if you're not above being cheap (and after a few fights against this guy, you won't be), you can use the Baby Maker to make him die like nothing:

The trick is to hit him fast with several Tediore explosive reloads before his shield is up.  He only turns aggressive and spawns a shield after taking damage, and you get enough time to murder him with this gun.  Bring full ammo.  This makes him only slightly less trivial than Terramorphous with The Bee and Conference Call. 
The Baby Maker drops from Madame von Bartlesby, the large Varkid boss in the southwest of Tundra Express, after you've beaten her for Tiny Tina's mission.  It's an orange/legendary Tediore Submachine gun.