Whirlpool islands are unlit, so having Flash as well is worthwhile. Having Pokémon with status affecting moves (i. e. Sleep, Paralysis, Frozen) is also very helpful. Bring plenty of Ultra Balls. Make sure your Pokémon are level 40 or greater. Bring plenty of Repels to avoid fighting pokemon along the way. A strong Electric or Ice-type Pokémon also helps.
Use Flash to light your way. Go up and then to the right. Continue right until you hit a wall. Go up and go down the ladder. Go down and stay on the path until you see another ladder to the right. Go down the ladder and go down and take the path on the right. Continue down until you reach the old man.
The battle will take place inside. You may want to save your game now.
Keep lots of potions and some PP Up, if you can. Have an Escape Rope ready so you can leave without going through the labyrinth again, and heal your party before going in.