Instructions
Place "Pokemon: Sapphire" or "Pokemon: Emerald" into the Game Boy Advance slot of the Nintendo DS. Turn on the system. In both games, you must first defeat the Elite Four.
Travel to the Marine Cave in "Pokemon: Emerald." You must first go to the weather center and speak to the man there to discover where the Marine Cave is located. It moves around during the game, and it can be found along Routes 105, 129, 125 and 127.
Move around the Marine Cave until you see Kyogre. Approach it to initiate battle. It appears at Level 70. Weaken Kyogre and capture it using a Master or Ultra ball.
Go to the Cave of Origin in "Pokemon: Sapphire," located north of Sootopolis City in the Hoenn region. Keep traveling through all of the floors. On the last floor, "B4F," you will see Kyogre. Go up to it to enter into battle, and repeat Step 3 to capture it. Kyogre appears at level 45. Place all other Pokemon except for Kyogre into the PC for storage.
Save your game and turn off the system. Insert "Pokemon: SoulSilver" into the DS slot of the Nintendo DS. Two games should now be in your system. Turn on the system.
Select the "Pal Park" option from the main menu of "SoulSilver." This will enable you to permanently transfer Kyogre to "SoulSilver."