Skills
You are not limited to the amount of skills you can bring into a dungeon. Learn as many as possible. The more skills you know, the better your chance of success. Support skills, such as Heal and Iron Body, can be important. Selling unwanted equipment and complete missions to save gold to spend on skills.
Upgrades
Train your hero by spending gold and waiting for them to complete their improvements. Afterwards, your hero will have a permanent boost to the stat that was selected to train. Strength, physical and magical defense are the most important stats to upgrade. Strength increases your auto attack damage, and physical and magical defense improve your defenses against those types of attacks.