Instructions
Pause your game and go to the Sphere Grid menu page. Teach Rikku every ability on the list by applying Ability Points you have earned in battle. You need to do this to unlock Bribe, the final ability.
Gather as much money, called Gil, as possible. Bribing monsters requires plenty of Gil. It takes 8,600 Gil to get a monster to drop two Mega Phoenixes.
Go to Bikanel Island and battle Alcyones. Alternatively, you can go to the Cavern of the Stolen Fayth to fight Ghosts.
Wait until it is Rikku's turn in battle. Select Bribe from her list of abilities. Select the Ghost or Alcyone you want to bribe.
Enter "8,600" at the prompt, when asked how much Gil you want to offer. The monster runs away, leaving behind two Mega Phoenixes in its place. Continue to bribe more monsters if you need more Mega Phoenixes.