Always plan for the new monsters taking immediate actions
Opening doors aggressively but safely is almost a mini-game. Always plan for the new monsters taking immediate actions. You want to be as healed up as possible and have as many ability and item card options available as possible before cracking open another room. Resting just before opening doors if you're almost due is often prudent. You may want to take a turn to cast some persistent buffs while you're not under enemy pressure. You'll want all your characters close to the door when it's opened so they can contribute quickly. But you don't want to waste too much time to get ready before opening every door. Try to have your door-opener reserve at least one extra hex of movement available to your after the door opens to either retreat or advance to a better tile. If you're a melee character, try to have either a ranged attack prepared or additional movement ready (boots) so you can immediately make some sort of impact. Know the rules for LOS between hexes, it actually takes quite a sharp angle for LOS to be blocked around doorways and more often than not both sides are easily targetable.
Avoid damage
Whenever possible, avoid damage that you don't have to take. As soon as the monsters' cards are flipped, carefully check which monsters are doing what, how soon, how hard, and at what range. If you can stay out of range, kill/stun/disarm/immobilize/muddle particularly troublesome actions, or avoid AoEs before they happen, do so. Sometimes it's even worth completely scrapping & replacing your original plan to avoid a single high damage attack or summon. Consider playing the opposite top & bottom, burning a card you didn't intend to, or just switching to a default attack and/or move. This is where playing the highest initiative you can more often than not becomes valuable. If you go first, you can avoid a lot of unexpected headaches by improvising. When you start to get good, you'll even begin choose your card combos with such alternate plans in mind already.
Earning extra XP
Don't worry too much about earning extra XP from actions, your first priority is winning, or you will lose all gains made anyway. You don't need a ton of gold, and only the treasure chests are worth going out of your way for. Leave most coins on the floor, unless they literally fall into your lap along the way, or you have a convenient moment of peace to play that Loot card. Only once you're in the last room, with most enemies under control, and confident of victory, you can afford to relax a bit and start grabbing coins and playing cards for maximum XP. Feel free to let the last guy live an extra turn while you grab what you can.
Manage your movement through the dungeon efficiently
Besides killing the baddies and avoiding damage, your third goal should be to manage your movement through the dungeon efficiently. Whenever reasonable, try to move closer to the next door while still doing and avoiding damage efficiently. Do not swap out/burn/use up your best movement cards lightly, having a reusable Move four or jump available can save you several precious turns over the course of a long dungeon. Movement items (boots, teleports) are very valuable not only to for maximizing attacks, but to speed your progress through the rooms.
Try to be proactive
Try to be proactive, not reactive. Offence usually trumps defence in this game, as you're on a card clock, but the monsters aren't. The best status effect is "dead". You can't hang back, shield & heal, as your resources are limited, and the enemy's are not. Some will summon more if given the chance. You won't have to prevent or heal damage that you can avoid or preempt through clever timing, positioning, card selection, and item use.