Upgrading Espers

From JDpedia

Upgrading your Esper increases its level. This makes its attacks more powerful and increases the bonuses it provides you. In order to upgrade your Esper, its proficiency must be at max. You can raise your Esper's proficiency by using its skill, which is automatically placed in the first slot of the Esper Bar, or by buying an Esrelic like Wyvern Blood or Dragon Blood from the cash shop and catalyzing it.

Once your Esper's proficiency is at max, go to the Esper Mystic. Move your Esper to your bag, then select the Esper Mystic's 'Upgrade' option. Drag the Esper to the slot and click on the 'Start' button. Your Esper should go up a level.

The upgrade will fail if the Esper doesn't have enough proficiency, if you don't have enough money, or if the Esper is at its max level.

Your Esper has a max level that is based off your current level. This limit is x/5+2, where x is your character level. Thus, at level three, your Esper's max level is 2. At level 10, your Esper's max level will be 4. At level 30, its max level will be 8.