Well, the most difficult way would be to defeat Nemesis at the Monster Arena. But, I don’t think you want to do that.
The easier way is to go to the Calm Lands. Fight a Chimera Brain there. Bribe him for at least 196,000 gil, and you should receive Lv. 4 Key Sphere x2, most of the time.
Dropped by – Seymour Flux (Mt. Gagazet)
– Spectral Keeper (Yevon Dome)
– Omega Weapon (Omega Ruins)
Rarely dropped by – Land Worm (Inside Sin)
Bribe – Chimera Brain (Calm Lands) (For 196.000 gil)
To cut the "chain" of the chests, I opened the first ones, went to the savepoint and restarted the game. Then I did the next chest, back to the savepoint etc. When you do this, the chests always start with "chest one" again, which means a new lv 4 key sphere.
And sometimes you�ll get some inside of Sin. 🙂