Level up your abilities as soon as you gain a new level. Spend gold coins when you ascend a new hero to unlock some new abilities and level them as high as possible.
Attacking
In order to win a battle as fast as possible, target weaker enemies first. Have as few enemies as possible remaining after each round. Also give priority to enemy healers to prevent them from negating a portion of your damage.
Elemental strengths
Red is stronger than Green. Green is stronger than Blue, etc. Tap the basic attack icon on the screen for each of your heroes and take note of the that appear above enemy heads. A green arrow indicates normal damage. A double green arrow indicates extra damage. A red arrow indicates reduced damage.
Hammers
Collect hammers to upgrade your base after reaching level 10 and PvP battles become available.
Special attacks
Each special attack has a cooldown. Plan out the number of turns until a Boss battle and make sure all your special attacks will be available. If you can use a special attack twice during a Boss battle you will have a significant advantage.
XP Potions
Save your XP Potions to when you get a rare heroes from summons or by normal game progression. Use them on those newly found heroes to level them up quickly. Replay earlier and easier stages to help max them out.
Abilities...