To defeat Jasmine -
Go upstairs in the lighthouse, till the end. You'll see an open window (the floor near it will be covered with shadow), go through it and you'll get to the reet of the building till you'll eventually get to her.
Talk to her, go get the SecretPotion from the "mart" in this island-city, go back to her and she'll go to the gym and challenge you.
P.S, for questions, PM>VM.