In Skyanders Ring of Heroes there are two ways in which you can level up your characters so you improve their stats. You can either get victories in Adventure mode stages or use red poitions.
Adventure Mode
Keep repeating the Adventure mode battles to grant your characters EXP whenever they are victorious.
Red Potions
These are obtained when you complete the quests given by the magic cauldron that is in the town.
Tip: Set the Adventure mode battles to auto if you don't have red potions.
To increase your characters skills you need upgrade stones and elemental ores. Elemental ores can be acquired from Distorted Dimension mode and must be the same element as the character. In Distorted Dimension mode you defeat the enemies in the following dungeons
You can power-up your characters to make them more powerful by using upgrade elixir and soul stones. Elixir is acquired from Distorted Dimensions mode.
To develop a character further once it has reached its maximum level you will have to evolve it. Soul stones are required for this procedure and once a character has been evolved its max level cap and stars will be increased allowing you to improve it further.
When you Awaken a character you will improve its skill and stats. Soul stones and high-rank elemental ores are needed to perform this procedure. The characters' Awakened forms in Ring of Heroes is similar to the SuperChargers versions of older Skylanders, where they gain a new outfit.