It helps a lot to take this fight on with proper armor on Cassandra (whom I take it is sword and shield). Don't hesitate to equip her with the highest armor value (300ish, or even 330ish if you can spare a 10% masterwork), helm value (50ish) and shield value (60ish) in your arsenal. Forget every stat but armor if you must, just make sure she's got the goods. The reason is, the punches deal a TON more damage sometimes so any delay in interruptions will force her to drink a potion. When it comes to Cassandra builds, make sure she has all the passive Armor bonuses and most of the Ogre attacks won't even scratch her.
Put Inky on Emissary camping duty. That's Inky's only duty in life for this fight: kill Emissaries, one after the other. Emissaries must not be shooting fire at Cassandra from behind when she's being grabbed, this kills the Cassandra. Since Barrier damage ignores Cassandra's armor, the Ogres are going to destroy her barrier leaving her vulnerable to Emissary fire, which will destroy her guard, leaving her vulnerable to Ogre punches, in a deadly cycle of death.
Emissaries have three attacks: shoot one bolt, shoot many bolts and shoot one super bolt. One bolt is cool. It can be tanked or avoided. "Many bolts" must be tanked and barriered/healed/guarded through (or you can try to hide behind a pillar if you're ranged). One Super Bolt has a charging animation where he charges up its Kamehameha, you need to move out of the way (roll behind him or charge through him), or suffer 120ish fire damage at maximum fire resists. It has only a short range, but it's another reason why Emissaries are bad news. On the plus side, as a Two Handed Templar, your Inquisitor is born to kill Emissaries - I doubt many classes can take them out as quickly and safely as you.
Also, there should only be one emissary at a time during this phase, so kill both emissaries outside before you go in, the other is probably a leftover from the previous phase and should not respawn.
So almost all barriers should go to Inky, Inky should solo kill Emissaries, and mages should simply grind down the Ogres and interrupt them when they grab Cassie. Ogres are immune to pretty much all status effects and they are greatly resistant to spirit, but walking bomb explosions still stun them during their punches, so Dorian can and should keep this one up on them, or even better, on the genlocks around them, because you never know, but otherwise, forget about spirit damage. You should probably equip another staff, if either Vivienne and Dorian are using spirit damage.
Once you're done with the Ogres, the true attrition fight begins, wher- oh nevermind you have two templars and two mages. Always dispel the large fire AOE debuff and you should be fine. Remember to finish the last Emissary after the Ogres before taking on the final boss.
Lastly, pro tip: you can run back to the entrance of the area (with the fires), get out of combat, change your inventory and even respec your build there, if needed.