Garchompite in Pokémon Radical Red

Starting from the Cerulean City Pokémon Center, take the path West.

You’ll see a house in the very Northwest part of the city. Head inside.

Inside the house, simply walk up and exit from the other side.

The backyard of the house is connected to a river. Use Surf to get on your Pokémon and follow the river going West.

You’ll shortly come across the entrance to the Cerulean Cave. If someone is blocking the entrance then you’ll first have to collect seven gym badges and then attempt to enter the Viridian City Gym to get access to the Cerulean Cave.

Inside the cave, you want to start by heading up.

You’ll come across some water. Use Surf here too to follow the water without landing anywhere else.

At the very end of this path, you’ll see some stairs you can use to get back on land.

Now you want to follow the path without taking any of the ladders you see on the way.

Eventually at the end of this path you’ll come across a ladder heading upstairs that’ll be on a separate platform.

Use it to go to the Cerulean Cave’s maze area.

Now you want to walk left and then go down as soon as you can.

Follow this path and you’ll get the choice to take one of three paths. Follow the path to the right.

Continue following the path, using Rock Smash to clear some rocks on the way, and you’ll eventually reach a ladder heading downstairs at the end of the path.

After going downstairs, you’ll see another ladder to your South that you want to take.

Get down from the platform you reach after taking the ladder using the stairs to your East and then continue going East.

You’ll eventually come across some smashable rocks in the Northeast part of the room, and the Garchompite will be behind them.