Capturing pillars and spawn points is what wins you maps, not knocking out other units. Get things set up to take control of one, including a character ready to dash out and sit on it for a turn, and you will win scenarios a lot faster.
Scenario descriptions
Pay attention to the scenario descriptions. The game rapidly branches out and it is easy to end up playing a level that is too tough for your current characters.
Struggling
If you are struggling with a level, take the time to learn what kinds of damage your foes dish out and are vulnerable to. Then re-jig your equipment and skills to take advantage.
