Im going to go out on a limb and say your talking about Pokemon HG/SS. You need to go north of Cerulean and follow the path to the end, battling all the trainers. You will find her there.
misty
In cerulean cities gym you must beat the leader misty to get the cascade badge.
You must go and battle Misty. Once you defeat her, she will give you a badge. You have then defeated the gym.
You need the second badge which is obtained by beating cerulean cities gym leader misty.
u must win 1-7 gym leader gym: brock misty lt.surge erika :defeat them all koga Sabrina blaine and Giovanni
* Pewter Gym - Rock Badge * Cerulean Gym - Cascade Badge * Vermillion Gym - Thunder Badge * Celadon Gym - Rainbow Badge * Fuchsia Gym - Soul Badge * Saffron Gym - Marsh Badge * Cinnabar Gym - Volcano Badge * Viridian Gym - Earth Badge
To obtain the Cascade Badge you will need to defeat Misty the Cerulean City gym leader in a pokemon battle.
In Pokemon FireRed, the badge needed to surf is the Cascade Badge. This badge is obtained by defeating Misty, the Cerulean City Gym Leader. Once you have the Cascade Badge, you can use the move Surf outside of battle to navigate bodies of water and access new areas in the game.
When he went to fight the Cerulean City gym leader, her 3 sisters were going to give him the badge without fighting, so she stepped up to uphold the honor of the gym.
1st badge: The Boulder Badge, given to you by Brock, the Rock-type gym leader of Pewter City. 2nd badge: The Cascade Badge, given to you by Misty, the Water-type gym leader of Cerulean City. 3rd badge: The Thunder Badge, given to you by Lt. Surge, the Electric-type gym leader of Vermillion City. 4th badge: The Rainbow Badge, given to you by Erika, the Grass-type gym leader of Celadon City. 5th badge: The Soul Badge, given to you by Koga, the Poison-type gym leader of Fushia City. 6th badge: The Marsh Badge, given to you by Sabrina the Psychic-type gym leader of Saffron City. 7th badge: The Volcano Badge, given to you by Blaine, the Fire-type gym leader of Cinnabar Island. 8th badge: The Earth Badge, given to you by Giovanni, the Ground-type gym leader and leader of Team Rocket from Viridian City.
defeat brock blaine misty ericka poison leader and all the other gym leaders
In Pokémon Silver, you need the Cascade Badge to use Whirlpool outside of battle. This badge is obtained after defeating Misty, the Cerulean City Gym Leader. Once you have the Cascade Badge, you can navigate through whirlpools in the water.