Be aggressive: The heroes are given the first chance to act in each room. If you can remove some of the starting monsters from the playmat on turn one each time, it will save you damage in the long run.
Coordinate: Plan out your turns in advance. Where do you want to end up? What monster do you want to focus on? Can you use your turn to push another hero into a more strategic position?
Don’t hold back: Abilities should be used early each room to maximize their effect. Spells and items should be used throughout the game. They will do you no good if you hold onto them until the very end — if you never make it to the end.