Instructions
Bribe the Chimera Brain fiend in the Calm Lands with 196,000 gil. Max out Rikku's sphere grid to obtain the "Bribe" function. Journey to the travel agency in the Calm Lands, where you should save before attempting this, since it does not have a 100 percent success rate. Engage in battle with a Chimera Brain located behind the travel agency toward the large spike in the ground, and use the Bribe option to end the battle. Give it 196,000 gil to end the battle, and hopefully it will give you two Level 4 Key Spheres in exchange. If it does not, reset the game and attempt it again. This can be done as many times as you like.
Open the treasure chest toward the top of the trail on Mount Gagazet. There will be two chests next to each other. One of them contains a Level 4 Key Sphere.
Defeat the Spectral Keeper in Zanarkand to receive a Level 4 Key Sphere. If the killing blow deals 8,000 damage, then you will land an Overkill, which will result in receiving double the amount of spheres.
Participate in the chest minigame near the entrance at the Omega Ruins. There are 12 treasure chests, displayed four at a time, with a one-in-four chance of getting a treasure, and a three-in-four chance of getting a monster. Successfully opening the first box will result in you getting a Level 4 Key Sphere. You could try to open treasure chests one through seven without triggering a monster, however there is an easier way to get the Key Spheres. After opening the first chest, leave the Omega Ruins and then return. The treasure chests reset each time, and each time the first chest has a Level 4 Key Sphere inside.
Defeat the Omega Weapon in the Omega Ruins to get three Level 4 Key Spheres. Defeating it with a killing blow of 13,600 will result in an Overkill, giving you six Level 4 Key Spheres.
Defeat Seymour Flux inside of Sin to get a Level 4 Key Sphere. If you land an Overkill blow of 3,500 to defeat him, you will receive two.
Capture 10 of each creature for the Monster Arena and defeat all the Monster Arena creations. In the Calm Lands, you have an option to begin a quest to help the man that is running the Monster Arena. Purchase weapons from him that have the ability to capture the fiend if you land a killing blow with the weapon. Defeat 10 of each non-boss fiend in the game. After doing all of that, you will have an opportunity to face off against a new creature, Nemesis. The Level 4 Key Sphere can be stolen from him.