Level 4 Key Spheres
One of the earliest things to road block you in Final Fantasy 10 will be Level 4 Key Sphere locks on the Sphere Grid. There's usually at least 2 or 3 of these blocking the way to extremely useful abilities like Doublecast or Full-life and amassing enough of these may be a bit confusing to those who are unfamiliar with the game.
Unlike the Level 1, 2 or 3 Key Spheres you're not going to want to farm monsters for these. Instead the most efficient way to get them is by bribing enemies. In particular, Chimera Brains which you can find in Calm Lands but we're going to hunt them in the Monster Arena instead!
If you are unfamiliar with Bribe and how to use it to get items from enemies I highly recommend you read up more on it. You can get almost all of the rare items you need for good Weapon Customization this way which makes it extremely important for min maxing your character's potential.
When it comes to farming the Level 4 Key Spheres what you'll want to do is first capture the Chimera Brains from the Calm Lands if you haven't already. At this point in time if you haven't already done so you may want to focus on capturing all the enemies for the Monster Arena as well, not just the Chimera Brains. For more information on doing that check out my Monster Arena Guide.
After you capture the Chimera Brain enemies from Calm Lands speak with the Arena organizer and scroll down the list to Calm Lands, select the Chimera Brain enemy and engage him in battle. If you haven't done much on the Sphere Grid yet you'll need to use Rikku for this part as she's most likely to be the character you have Bribe on.
You will want to hand the Chimera Brain 196,000 as seen in the screenshot above and this will end the fight. Your reward will be 2 Level 4 Key Spheres. It's an extremely costly endeavour but it's the most reliable way to acquire all of the Level 4 Key Spheres you could ever need.
Sometimes you'll have to hand him more than 196,000 otherwise he'll just eat your money and nothing happens. I always used save states before handing him any Gil and I always handed him an even 200k which saved me time scrolling over and down a few spaces. Not really sure why sometimes he takes more and sometimes he takes less!
Monsters that drop Level 4 Key Spheres:
Spectral Keeper (Zanarkand Ruins)
Land Worm (Inside Sin)
Monsters that you can Bribe/Steal Level 4 Key Spheres from:
Chimera Brain (Calm Lands) - 196,000gil for 2
Some Locations you can find Level 4 Key Spheres:
Gagazet: Mountain Trail (Chest)
Inside Sin: City of Dying Dreams (Chest)
Omega Ruins (Random Chests)