Everything Raleel said plus...
RE: Environments
In Lords of the Ash we have a new combatant type which is the environment. It gets it own initiative tile(s) and during the environment's turn "stuff" happens.
Knockback
Power Over Wind and similar powers will isolate a combatant rather easily. Dark Juxtaposition also works well.
Shroud
Remember that Shroud works both ways, so a Shrouded dweller will be harder to heal with targeted (non-Ara) Heal powers.
Denizen Mix
If you feel comfortable, try and use more than one type of enemy. A good party mix of denizens will prove much more challenging than predictable powers on X denizens.
Use generic actions
Place your enemies adjacent to dweller casters and poke/interrupt their spells. Go last in the round, and grab the warrior's weapon? No runes left to counter the grab? Too bad!

Note: If you find a vulnerability, don't exploit it over and over again. Grabbing a warrior's main weapon is hillarious the first time you do it, but starts to become annoying if it keeps happening every combat.