PeakTop
Let me add my two cents.
I managed to complete that infamous first mission on my third try, thanks to an interesting bug (or maybe it wasn't a bug at all). But let's go through it step by step:
1) Neutrals and liberating cities weren't a problem for me. What I struggled with the most were the blue heroes with armies 2-3 times larger than mine and terrifying hordes of Cyclops and Ogres.
2) I found myself in an endless loop: I would capture a city, move on to take another, and the blue faction would immediately recapture the previous one. At the same time, I was constantly losing troops, while the blue faction was increasing theirs, as they usually had 1-2 more cities due to the number of heroes and because in the first few weeks, I had almost depleted my reserves fighting neutrals.
3) But I got lucky with that bug. Or maybe it was just an AI flaw. In short, the computer for some reason really doesn't like it when I capture its buildings with Cyclops and Ogres. It immediately leaves the city to reclaim the building. And this can be used to direct it where and when we need it. After leading it around for a while and catching two relatively weak troops, I managed to capture 3/4 of the cities (two Dungeon cities and one at the very top, which we get for the ore cart).
After that, the situation developed so that I was standing with an army not far from the last blue city, one thief was guarding the Cyclops and Ogre dwellings, and the AI refused to leave the city, presumably fearing to lose it. Well, after that, victory was just a matter of time. After waiting for a few weeks (to avoid messing anything up) and gathering some reinforcements, I moved in for the assault and completed the scenario.
It's possible that the size of your troops won't be enough to intimidate the blue faction to the point where it stops leaving its cities, or that one of its armies will survive and constantly recapture your cities. In that case, I would keep the northern Dungeon city (as it's the only city with a stronghold and level 3 buildings) and use two thieves to control the Cyclops caves and the Ogre dwelling, buying up the reinforcements with caravans. Then, again, we gather a strong army and start taking them out.
