When I was playing this mission, I immediately tried to clear the area around my castles as quickly as possible and build up the castles themselves. I only built upgraded dwellings in the eastern castle to save resources. A support hero (I almost wrote "caravans") delivered troops from the western castle to upgrade the units.
As soon as I saw a Necromancer in the tavern, I immediately bought him. Then, support heroes delivered troops to him from all the Necromancer castles.
When I collected the necessary artifacts, I took them to the prophet and received Phoenixes. I left them in the castle so that the mission wouldn't end too quickly.
Nicholas didn't go into the Dungeon. Perhaps this was because a Necromancer with a huge army was nearby, just in case, near Faidan. When they surfaced into Nicholas's territory, the Necromancer had over 180 dragons. Faidan also had a considerable army from two castles. All the enemies immediately hid in their castles.
I only upgraded Chaos magic for Faidan. In this mission, a rain of charged Magic Damage or a volley of three spells worked very well against the three sworn enemies. However, before the final battle with the Overlord, there was nowhere to designate sworn enemies.