>>36148875Pokemon tournament.
Basically, you enroll in the tournament and participate in different stages in different cities. As you reach higher stages, the opponents become stronger, naturally. You lose and you need to start over in that city (realistically you should be disqualified and you'd have to start from the beginning in the following season, but that'd be incredibly tedious).
All stages include battling, at least 3-4 battles. But they also include other challenges.
There are gyms and gym leaders, but leaders are pro's. Just below the E4, all of them. You can challenge them once you win the tournament. Then you can go face the E4 and champion