Instructions
Obtain a Pokemon that knows the False Swipe move. Pokemon like Scyther, Marowak and Farfetch'd learn False Swipe when they level up.
Get a Pokemon that knows a sleep-inducing move, like Hypnosis. Many dark and ghost-type Pokemon learn this move. If desired, find a Pokemon that knows a paralyzing move. Electric types often have the ability to paralyze foes.
Stock up on Ultra Balls and Timer Balls. Ultra Balls have the best catch rate of all normal Poke Balls. Timer Balls work best after many turns pass in a battle.
Go to the Hidden Tower to confront Kyogre. Attack Kyogre a few times using your strongest Pokemon and then use the False Swipe move. If it hits, Kyogre has just one HP left.
Use a paralyzing move on Kyogre to reduce his speed and prevent him from moving. When he is paralyzed, use the sleep-inducing move on Kyogre. It may take several turns for Kyogre to fall asleep, depending on the accuracy of the move you are using.
Throw an Ultra Ball at Kyogre. If you do not catch him the first time, keep throwing Ultra Balls until he wakes up. Put Kyogre back to sleep as soon as you are able.
Start using Timer Balls if the battle goes past 30 turns. At this time, you have a better chance of catching Kyogre with a Timer Ball.