I think it's important to differentiate between a battle oriented goal and the character battling.-It's possible for Liko not to have a battle active goal but still battle in nearly every episode. She might be portrayed as the type of character who doesn't like initiating battle but is willing to fight if it means protecting others or if some obstacle is in the way of her main goal. For example, she might need to acquire a rare item but the only way to do so is enter a competition. Not wanting to become a powerful trainer, capturing legendaries or whatever else doesn't prevent her from battling the antagonists, the wild Pokemon of the week, or helping her Pokemon evolve or learn new moves.
Regardless her goal, Liko will likely battle a lot. She joins a research group, but they have a rival group that they will surely fight with. She seems to have a rival in a Amethio.
That said, I doubt Liko's goal will be battle oriented. Her goal seems to be related to discovering the mysteries of the pendant.