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I registered just to respond; I'm playing on War and have completed two missions.
The first mission wasn't particularly difficult. I cleared out almost all the resource nodes in the underground, except for two. After moving to the surface, it wasn't immediately clear what to do because my army was still small, making it hard to clear out many resource nodes. Then I found portals and started running around in circles, gradually clearing out the nodes. When I had enough strength, I started clearing out the garrisons. In the end, I arrived with an army of 1,000 archers, 150 vampires, 60 liches, and a few other units.
I had to replay the second mission because I didn't complete the quest with the traitor on my first attempt. I was also lucky enough to find a Lich on weeks 2-3, and I managed to capture several stacks. After capturing the second castle, it became much easier because I had already defeated the enemy's main army and all the other heroes. So, for the rest of the mission, I fought against neutral creatures. I cleared out only one dungeon with a curse (the first one); I tried the others, but I didn't bother because I lost too many units, and the curse didn't have much of an impact anyway due to the artifacts I had. I tried to dig up the Tear, but I think it's impossible to dig it up if you don't find all the obelisks.
Now I'm stuck on the third mission. I've tried it several times, but I always fail because I spend too much time on the starting location and don't go to the garrisons. Each time, I complete the catapult quest. Now, I'm trying a more aggressive approach. In the first week, I cleared out some of the starting locations, including the orc buildings, to replenish Goth's army. I also cleared out almost all the resource nodes near Zehir on the way to the castle and at the gates. After that, I used Zehir and Goth to clear out the garrisons, and later I brought in Freya. I cleared out all the garrisons (I didn't make it before the first reinforcement arrived, but I did before the second), about half of the Dwellings, and the simple resource nodes along the way. But I still don't have enough strength to be on equal footing with Shadowmancer. Maybe I need to rush earlier to avoid losing the first reinforcement, or maybe I need to find a better build order. The map is quite narrow, and caravans get stuck easily. I think a Temple would be useful on the right side.