I hate, hate, hate this map! Most of your enemies are Inferno, which is not exactly bad, because if you have Arachne equipped, you have a free "mass life drain". The problem lies in their towns. If they have their special building built you will be taking damage for each turn you are outside of the towns. Which is where "mass haste" comes into play for all your Dragons, Manticore/Scorpicore, and Faceless. At least someof your units won't be hit every turn. Also, late in the game you can finish up the Assassin set (if you've followed my walkthrough), which helps your creatures avoid attacks. If you don't have "haste", however, the best bet is to use the best artifacts for each slot instead. So look for "mass haste" scrolls.

You will not have enough money or resources ever, even if you took all resource Dynasty Traits. Also, finally there is a Tear in this quest. Makes your creature growth pretty insane.
Dynasty Traits +3 Movement, +10% gold from all sources, +3 Core, +1 Elite, Better prices at the market for resources (eventually this loses its effect as you will have so many marketplaces so you can substitute... but I think it is very handy early in the game).

You start out in Town A. Again I would advise you to get a might hero day one for ore/wood and to help flag/pick up items. Yes, you have one hero, but it is very difficult to flag both starting mines with one secondary hero. Plus, you need all the ore/wood you can get. At a1 there are some Stalkers to pick up, who tell you that at 1, there is a gate from which inferno units are being summoned. Time to do some curb stomping.
Finish off the Inferno troops, then immediately claim Fort B. You will get a cutscene showing you 3 where yet another gate is (at the b1, b2 and b3 there are Arcane Libraries that you need to visit in order to close this portal).

(click image to enlarge)

This triggers ‘The Prince of Chaos’ to come your way. If you hit the observation tower you will see a training center at a2 and get a quest to rebuild it. You don't really need it, but the reward is nice... if you can find the resources to do it. You can pick up your first Moondisk Fragment here. Go clear out the area and claim Fort C and another Moondisk Fragment. This seems to trigger Haven heroes coming from 2 (it might also be at a certain time, I was not paying attention). There will be two waves. If needed, summon your secondary hero to Fort B to reinforce your main hero, or gate your main hero back to your main town and upgrade, then port to the fort and head north after dealing with the first Haven hero. At 4 you will find another stationary Inferno army (not ‘The Prince of Chaos’), who is pestering some Manticores, Faceless, and Minotaurs. If you've upgraded these, make sure to have a secondary hero following your main hero in order to pick them up. I actually advise not to upgrade them until you have claimed these stacks. Saves a lot of hassle of having to gate back to upgrade them to fit into your army.

Keeping a careful watch out for the Prince, head for Town D. In all the times I've played, this town always has a Moondisk Fragment on its main hero. I think it is scripted that way. Also claim the Arcane Library while you are here. As long as you are not hounded by the Prince, start making your way to Fort E, might as well claim the last Moondisk Fragment on your way... and once you have claimed Fort E, time to go back to your main town.
Now, even if Town D has an Advanced Portal, as long as your main town does also, there is a way to make sure you port to your main town. Just have two secondary heroes in Town D. Since there is no room, your main guy will instead go to your main town. Either leave the tear here with a secondary hero, or if you can afford it... build the Tear Building. You get no "summon phoenix" disk this time.

Head towards Town F as soon as possible, and also claim the second Arcane Library here. The way to Town J is blocked, so head towards Fort G. Claim it, summon backup via a secondary hero, and head towards Town H. Once you claim the Arcane Library here, you still have to visit 3 in order to close it. Closing it opens up the doors to Town J. The people from this town seem pretty stationary, so if there are none left from the gate at 3, you can take your time and build your army up, clearing the rest of the map. Visit Town F on day one, buying every last creature you can. Sell all excess artifacts that your hero will not be wearing to build your cash up.

Then... rush Town J.