Shadow Dragons -how to beat them?

Given that they have no defense against Elemental or Death magic, I would recommend some good magic damage dealers. Temple units would be best. Enchant your units with damage increasing enchantments too.
Your real objective should be to get them to stop spawning. If you're in exiled mode, you should focus on completing the world you're on, Ainadra or Ardania.

-If you're on Ainadra, clear the Citadel. But don't go through the portal yet, or the monsters will start spawning again. Wait until you're ready.

-If you're on Ardania, focus on killing the lieutenants.

Another thing you can do to stop things from spawning, terraform the unused tiles in and near your territory into water or mountains. If there is no place for the lairs, they won't spawn.

Yeah you gotta nuke them pretty hard, which is pretty tough, but they have no defence. They are also not immune to banes, so inevitability will stun them if you can't nuke them.

Fungi127 said:

They are also not immune to banes, so inevitability will stun them if you can't nuke them.

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Though that only works if you have the spell pack DLC.

Now that they've put all of the spell packs into one 4.99 DLC, it's definitely worth it. It contains 15 spells, some of them boring, but a good number are interesting and useful. Such as inevitability mentioned above, stuns the target. Very useful for keeping powerful enemies from attacking you. Provided they are not immune to banes.

Shidan covered all the major things i wanted to say. Only thing left out is the souped up artifacts and spell buffs you can enchant your lords with. If you are playing undead krypta has the best weapon enchant in the game imho. 50% life steal and Death damage is amazing, Give your lord invisibility, levitation and ton's of resistance and you're set to kill anything with 1 unit.