You can level up the acquired Hero by using the other Hero characters as the materials or through exploring the Adventures.
To level up your Hero using other heroes as level up material,
- Go to Hero menu
- Select the Hero you want to level up
- Tap Grow
- Select the material heroes from Heroes on Reserve
- Tap Grow on the right bottom.
Note: You would also need Gold to level up your Hero.
You may also level up your Hero by using EXP character acquired by defeating the Hero summoned in Hall of Heroes.