Instructions
Getting Strength
Travel to Mauville City, which is north on Route 110, south on Route 111, east on Route 117 and west on Route 118.
Enter the Gym, located in the middle of town, and speak with the gym leader, Wattson, to start a battle. After defeating him, he'll give you several rewards, including the Rock Smash skill.
Go to Verdanturf Town, which is west on Route 117. From there, head north to the Rusturf Tunnel. Inside you'll find a man and his spouse separated by a boulder. Use Rock Smash on it and he'll give you the skill Strength.
Getting to the Icy Floor
Go to Shoal Cave, which is along Route 125. Time your trip so that you arrive between 3 am and 9 am or 3 pm to 9 pm. These are the low tide periods.
Enter Shoal Cave and then go through the middle cave entrance. This entrance is only available during low tide.
Follow the path. Eventually, you'll come across a series of cliffs with boulders. Use Strength to push them away. After the boulders you'll find another cave entrance. This is the entrance to the Icy Floor.