Instructions
Defeat the leader of the Sootopolis Gym and talk to the man standing at the mouth of the Cave of Origins to enter. The Cave of Origins is located on the north end of Sootopolis City. The elder protecting the cave will not allow you to enter without presenting the local Gym's badge.
Enter the Cave of Origins and walk down the linear path to the bottom level to find Kyogre. Kyogre is waiting in the fourth basement level and will not attack you unless it is approached.
Weaken Kyogre with Electric and Grass-type attacks until its health meter is blinking red. Throw Pokeballs at the beast to capture it. Kyogre becomes more susceptible to being caught if your Pokemon afflict it with either the "Sleep" or "Paralysis" ailments.
Defeat the Elite Four after earning all eight Pokemon Gym badges.
Climb to the Sky Pillar to find Rayquaza. Sky Pillar is located on the northern end of Route 131. Players will need to use the Mach Bike's speed to ride over the crumbling floor to get to the sixth level of Sky Pillar.
Encounter Rayquaza at the top of the Sky Pillar and attack it with Rock, Ice or Dragon-type attacks to greatly weaken it. Rayquaza appears at a strong Level 70 Flying and Dragon-type and players should use similar tactics to capture it as they did Kyogre.