What feature do you mean? Hero evolve, or hero upgrade? If you mean the Season Trial, then that doesn’t level up hero skills, but it does increase hero stats. You increase a hero’s season trial level by using them in fights with wild monsters on the map, this gives you cards for the hero, and you can use these cards to upgrade the hero’s stats in Hero Training.
However, you typically increase the level of a hero’s skills through either hero evolve, that unlocks and develops a hero’s passive skills, or through hero upgrade, that offers a comparatively small boost to the hero’s active skill when it levels up.
It’s difficult to tell what feature you mean exactly, however.