The Absolute Conqueror is a stronger version of the final boss, only appearing if you have done the achievement "The Final Instance" on the same save file. He has 1,000,000 HP and will eventually go into Overdrive where he attacks five times every turn he has (which will show up more than once if you have multiple unions deadlocked on him).
The most successful way of defeating him is using one super-union comprised of only leaders, using a strong formation called Dragontail II. To get this formation, you first need to complete Union of the Golden Chalice Guild Task 57 to receive the Rattail formation by obtaining a Divine Francisca weapon. To get this, hire the soldier Chamberland and just leave him in your reserves. He comes equipped with a Francisca and will eventually upgrade it to a Divine version.
Once you have Rattail, go to the Ancient Ruins and unlock every chest to receive both Foxtail and Dragontail upgrades. Now you can make your super-union. Be sure to have all weapon art users in the union and that your health is almost to max. I only had about 9.4k, but I used Rush, Torgal, Caedmon, Baulson and Blocter. You are going to need to conserve some AP during the first section against the two weaklings and hope they don't use Kilohit or Catapult to damage you much. Going into the fight with the Conquerer himself (and don't be alarmed, his name won't actually change to "Absolute Conquerer" it will still just say "The Conquerer") get your health up after he uses his Fatal Eclipse, then hope you get some good command prompts.
When I did this, I got two Talisman protection prompts, a dual-Heaven's Door attack with Baulson/Caedmon, an Ominstrike and about six Defense Triggers that did 50-90k each. Someone else who killed him in two turns got a quad-weapon art turn worth 700k. I personally took a slower approach and killed him in 5 turns. You want to try and kill him before he goes into Overdrive, or do like I did and kill him on his 5th attack during Overdrive (that would have wiped me) with a Defense Trigger. That is obviously not going to happen often, so aim for a high BR and crush him quickly instead. Equip anything that will raise your AP so you can always have a good amount to use on weapon arts. Mine was relatively low, which is why I had to rely on Defense Triggers and Talismans.