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These three skills are essential for unlocking the Regis. You can get Dig from the Fossil Maniac's brother on Route 114. You get HM03 (Surf) for defeating Norman, the Petalburg Gym leader. Dive can be obtained from Steven in Mossdeep City. You'll need to have beaten at least the first seven gyms to be able to access all of the moves you need to get the Regis. After defeating Tate & Liza in Mossdeep Gym, you'll gain the ability to use Dive in deep water. This is the last necessary skill to unlock the Regis. This is a rare Pokémon that can only be found in Underwater areas. In Ruby and Sapphire, use Dive on Route 124 and 126 to try to encounter a Relicanth, which has a 5% chance of appearing. In Alpha Sapphire and Omega Ruby, you can find additional Underwater areas on Routes 107, 129, and 130. There are also several underwater areas scattered throughout the world. You can fish for Wailmer in most areas in the game. Once you level Wailmer up to level 40, it will evolve into Wailord. You can also try to catch a Wailord by surfing around on Route 129, though it only has a 1% chance of appearing.

Summary:
Bring along Pokémon that know Dig, Surf, and Dive. Beat the seventh Gym. Catch a Relicanth. Catch or evolve a Wailord.