Did you encounter a boss you can't beat? You may have to change your tactics to beat that particular enemy. Here's a few tips:
Strengthen your heroes
Usually if a boss feels too hard, the answer is to develop your party further by grinding the earlier dungeons, and possibly capturing some heroes with special skills that work particularly well against this boss.
Enemies with high defense
Enemies like Skeleton or CXRin the Royal Palace can be tough to beat. You can see most of their health bar covered with gray defense. It's hard to do damage to these enemies, and you will need something to get through their armor. You need armor-breaking Hero Skills that reduce enemy armor, or Piercing Runes that you get from chests in Chapter 6. Also, skills that burn, poison, or corrupt the enemy can deal damage despite the armor.
Enemies that burn, poison or corrupt
You can obtain potions from chests to cure these effects, or use a Hero whose leader skill makes you immune to effects like burn.
When should you use healing heroes?
If you are stuck and you haven't tried healing Hero Skills, that might be the answer to surviving the dungeon. However, healing heroes do less damage than other heroes, so if you already tried healer heroes and it didn't work, then perhaps you should try heroes with stronger attacking skills.
The best way to learn the tricks and tips is to join a guild and ask your guild mates for pointers on how to beat each boss.