Now that you have the SecretPotion, go up the elevator of the lighthouse to give it to Amphy. Once you do, Jasmine will be appreciative and will go to the gym.

She, the steely-hearted girl, uses Steel pokémon. Not much can hurt them, except for fire, fighting, and ground moves. Steel moves are super-effective against Ice and Rock pokémon, so don't bring those.

Once you defeat her, you get the Mineral Badge. It allows you to train pokémon up to level 70 who still obey you.

There is not much else to do here. You can take a look at the place where the S.S. Aqua is. You can't use it yet, but you will later.

After you check things out here, go to Ecruteak.