The most challenging campaign.

I would like to ask if anyone has completed the third mission, "Conquest," of the Inferno (Hero: Agrael) campaign in Heroes 5 (without expansions) on Veteran difficulty. I've tried about 20 times. Please let me know if you've succeeded, as I suspect it might be a bug or a flaw in the game's design.

It's not that difficult; the main thing is to develop the right strategy.
I completed it in the following order:
1. For the first week, I focused on developing the Inferno Castle (market, warehouse, drilling for Imps and Demons). In the middle of the second week, I defeated Gilraen and headed straight for the nearest Elven Castle (Vinlan, I think) – the main goal is to capture it before the end of the second week. Then, I recruited a second hero (preferably an Elf) and followed this scheme: Agrael defeats the monsters, leaving the loot and mines for the second hero. I didn't develop the Inferno; I focused all my efforts on building the Elven Castle.
By the beginning of the second month, Gilraen will arrive. I couldn't defeat his army, so I took as much as I could from the castle and led Agrael along the road to the northwest, and the second hero back to the Inferno Castle. Gilraen, ideally, will capture the castle and immediately follow Agrael (Logistics helped me here; my Agrael could always move a good distance ahead of the pursuit). Agrael reaches the castle in the northwest and captures it; at the same time, the second hero, if he's lucky, will reclaim the southern city if Vinlan remains undefended.
After capturing the northwestern castle, Agrael heads northeast and destroys the Druids – this is important; after this, Gilraen's troops will no longer increase by 100 times, making it easier. Then, continue to the northeast and destroy the third castle. Gilraen will continue to capture the southern and northwestern cities – skillfully lead the hero away, taking the reinforcements from the cities whenever possible.
After that, I had a tedious month of running away from Gilraen, retaking cities, and gathering an army. When the time for the battle comes, it's important to "lure" the annoying Elf and lead him into a city – that's where you can engage in battle. In my case, he had a 1.5x advantage in manpower, but he casts all sorts of nonsense, and you need to take advantage of that. A well-placed army (don't let dragons get close to archers and druids) and the spells "Phantom" and "Berserk" will help (a scroll with it is located near the northwestern city, guarded by a decent number of Emerald Dragons).
That's how I did it; good luck!