Pokémon Gold and Silver/Olivine Gym

After you get back from Cianwood, go to Jasmine in the lighthouse and give her the medicine for Ampharos. She will return to her gym after healing Ampharos, and you can challenge her there. She uses the Steel-type Pokémon so Fire and Ground are two recommended types to fight her with, since both types of moves are super effective against her team.

After you defeat Jasmine, you'll receive the Mineral Badge and (TM 23).