My couple o' tips:
1. Pay attention to the elemental "base" of the enemies. For instance, those self-healing acid spewing zombie pigs are Earth-based. In this game, the opposite of Earth is Air, so air-based spells and weapon attacks will likely give you higher damage for your attacks, and will make them further susceptible to the extra stun / knockdown / whatever effects from your attack.
2. Based on the above, make sure your melee fighters have a variety of elemental weapons at hand. Nothing worse than using an Earth weapon on the zombie pigs, only to find that you're healing them along with every hit. Took me a while to figure that one out! "Would you DIE already?!? Oh crap - I've been healing him." heh
3. Same thing for characters like Jahan, who can use a staff to cast a lower-damage, lower-AP, never-miss ranged attack: be sure to equip the correct elemental staff according to who you'll be fighting.
Those are really apparent when you fight fire-based creatures with water attacks. I've seen a weapon's elemental bonus, which is usually just a fraction of the regular damage, cause as much damage as the physical attack when used against a susceptible enemy.
4. How do I know to which element the enemy is attuned? Scout their surroundings. Fire-based guys have lots of flaming stuff around. Go figure. Earth-based will have puddles of acid on the ground. Etc. You can also get a hint by the types of barrels nearby: there are often barrels of the type opposite the enemy's elemental alignment. For instance, if you're up against fire guys, you'll likely find water barrels in the vicinity. If you need to, use Telekinesis to move barrels to strategic points on the battlefield before the fight starts.
5. Note that you can cast spells before combat starts, but the timer is running as soon as you cast so you might have only one or two spells still active by the time you move forward to initiate combat. One thing I do is to cast the rain spell to get everyone wet - unless I'm going to be fighting Water (and maybe Air) enemies. This can weaken fire-based guys, and also sets me up for freezing them in one shot since they're already Wet.
6. You can also initiate combat out-of-range by using a ranged attack.
7. The Teleport spell can be used for a double (even triple) whammy: The enemy takes crushing damage upon landing, you can move the enemy close to a melee fighter who has yet to attack for that turn or you can move the enemy farther away from you so they waste APs moving back into range, and you can land them on an element that will cause added damage or other effects. With regard to the last, during a fight I had accidentally (and fortuitously) electrified a puddle of water, so when I teleported one enemy I had him land in the puddle. Crush damage, plus the charged puddle stunned him and took him out of the fight for two turns. Since I landed him on the edge of the puddle, my melee fighters could attack the stunned enemy without suffering negative effects themselves, and with 100% chance to hit.
8. Also try to cover your bases with the physical damage types. I'm seeing Slashing, Piercing, and Crushing, and some enemies are either resistant or susceptible to one or more of those. For instance, Crushing is the way to go with Skeletons, so keep club-type weapons handy and equip them before you start a fight. Be aware of the elemental damage, though, so your crushing weapon isn't also healing them via the element on the club. Gotta pay attention to the trade-offs.
9. How do you know which physical damage type they like / hate? Trial-and-error is one way. When you hit, take note of which type you're using and how much damage you're causing. The actual damage is shown in red, and then it will also tell you how much was absorbed. If the Absorbed number is high, then you should probably switch to a different damage type unless the enemy has some special defense activated. This is also when you take note of the elemental damage you're inflicting, to see whether you have the correct element equipped (assuming that weapon has an affiliated element). If you have trouble noting all of the damage info, scroll through the combat log since that will detail the damage results. Note that this is how I figured out I was healing enemies with my elemental attacks.
10. Try to have a no-miss attack available for each character. For instance, Jahan has Head Vice, Blitz Bolt, and his ranged staff attack that will always hit. Bow-users have at least a couple always-hit skill attacks available through skill purchase (but with cool-down times). Pure melee users are tougher to do this with, so you might also want to make sure they have a staff in the inventory for that ranged Source Hunter attack.
