chaos is brutally overpowered... you can send a 30 bolts attack (which means at least 10 bolts will always pierce the enemy´s defense) and use a spell that gives damage proportional to the number of bolts (so, at 10 damage, you have about 550 unblockable damage)
i got the badge with a Celestial Lightwielder. The first ten floors, you are immortal if using sanctify. Boost willpower (and a little str and int, but not sta!) and go melee + healing. Charm is nice for crowd control, as your mana should be very high because of the willpower (and charm doesnt needs much intellect, as the damage spells do, and it can save you from those blue-floor-sliding-guys)
if you stay very close to the final boss, right between two cannons (or whatever they are) you are inmune to the one of the attacks (the crossing mini-shots + extra bigger shots one)
Maybe it was karma after losing 30 times, but my winning strategy in harder was getting a lab as soon as possible and research the two techs that give bonus damage. After that, the odds of winning a battle greatly increase and you can clean almost safely the red squares with three or four soldiers. Balance defense and offense, as killing the neighbour enemies raises your defense (in some point, you should continuously send killing missions to every surrounding square). After certain point of expansion you become unstoppable, no matter how many dogs die.
Tips:
-Try to rescue the unrescued survivors if you can, rather than claiming the land. Also, research the bonus chance to find them before spying the whole world. You need cannon fodder.
-The white shirt survivors have a nice chance to become soldiers just by staying in the fort
-More soldiers = more zombie casualties (useful in late game)
-Bad luck in early stages or a lousy city map = death
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