In order to get the rest of the Trainers to fight you, you're going to need to solve some puzzles. These puzzles are based on notes hidden inside of books and following clues around. It's not overly difficult, but you can also just follow these directions to get through:
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You cannot re-battle the Gym Leaders in Pokémon Black and White.
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You get to the second gym by traveling through the Union Cave. Once through, you will reach Azalea Town. That town is home to the second gym.
good question, well i got white and there like the same thing. after you see N in the place after you beat the seneth gym. you fly back to the second gym and the gym leader there will give it to you.
No unfortunately :(