You can upgrade your heroes by Promoting or Evolving a hero.
Each rank gives an increase to the Hero’s base and maximum Special Ability levels, the number of elixirs they can consume, and their maximum level. Evolving a hero is unlocked after reaching a certain level that is determined by which character you are using.
You can either promote a hero simply by grinding in battle, or by using level-up items. These items are Gold, Power source, and Essence. Materials can be gained by playing, selling duplicate heroes, in the secret shop, and in the marketplace gateway.
Note: The secret shop requires a bribe of gems to enter.
Your upgrade level is limited to the level of your Headquarters. Your Headquarters (HQ) is available after completing levels 1-4 and stores all normal items you collect in a Treasury. Upgrading your HQ will increase the Max Hero level. Each new upgrade level requires a specific experience level, plus occasionally gems. So at HQ level 1, you can level your heroes to 10, but at level 2, you can level up your heroes to 15, etc.