Race for Rank!
Once you have a Green or Blue Chocobo, you’ll want to start looking towards the next color, an amalgamation of the two; the Black Chocobo. To get this critter, however, you’ll have to race, so that’ll be discussed now. With some Chocobos in your stables, head over to the Gold Saucer.
Note: You’ll need to have Cloud back in your party after the events at the North Cave, so if you must, complete the quests for the Huge Materia at North Corel and Fort Condor. If you haven’t progressed far enough, the Gold Saucer will be closed.
Note: Make sure you’ve fed your Chocobos! Unless you’ve boosted their stats with Sylkis Greens, their stats will be nowhere near their full potential. Worse, the birds will be so temperamental and stupid, they won’t race effectively.
Head to the Chocobo Square and talk to Ester, who should be standing near a door left of the central, circular race registry station and ask to race. Pick your mount and course (the short course will naturally take less time), then… well, win the race. To win pretty much every race in which your Chocobo isn’t simply massively outclassed just switch from Automatic to Manual control, speed up as fast as you can, and hold down the R1 + L1 buttons (Page Up + Target on the PC), which will cause you to regenerate stamina while you run. Sprint near the end of the race (past the wooden bridge leading to the blue crystal final run) if necessary.
Every time you win a race you’ll earn rank specific prizes, which can be taken, or redeemed for GP. In the latter case, this will fund your future ventures in the Battle Square, so be sure to redeem all the mundane loot you can buy elsewhere! Anyways, there are four ranks your Chocobos can be; starting with C-Rank, B-Rank, A-Rank and finally S-Rank. Every time you win three ranks your Chocobo’s rank will increase, which improves their breeding stock. Given the latent capabilities of Good and Great Chocobos, you should only expect them to reach (but not be competitive in) A-Rank. Green and Blue Chocobos might reach (but again not compete in) S-Rank.
For this venture, however, you really only need to get your Blue and Green Chocobos to A-Rank (but getting to S-Rank won’t hurt, if possible!).
Breeding the Black Chocobo
Once you have A-Rank or S-Rank Green and Blue Chocobos, return to the farm and breed your high-ranking Blue and Green Chocobos, feeding them a Carob Nut in the process. With any luck you should find yourself the new owner of a Black Chocobo; capable of crossing rivers, shallow water, AND mountains! This will allow you to cross a river to the north-west of Costa del Sol, where you can find the barren plains that houses the cave containing the HP MP Materia.
Going for Gold
The Black Chocobo is a fine mount, but the mightiest of Materia still waits out of reach… what you need is a Chocobo that can cross oceans, and you have most of the tools you need! Most, but not all, however. You’ll need to acquire a new type of nut and capture a new grade of Chocobo; the Wonderful Chocobo.
First things first, fly to some islands stranded in the north-eastern corner of the world map, Goblin Island. Land on the one with forests and enter the woods, where you can encounter Goblins. They’re not as sturdy as the Vlakorados was, so be careful as you attempt to steal a Zeio Nut from them. You should only need one.
Once done, make your way to the snowy western half of the northern continent to find some Chocobo tracks south of Icicle Inn. Here you can find the Wonderful Chocobo, who keeps company only with "Jumping" enemies; big white rabbits that have a frustrating tendency to dodge attacks. Still, kill the bunny bodyguards and you’ll score yourself a Wonderful Chocobo. Catch one that’s the opposite gender of your Black Chocobo, feed them Sylkis Greens, then race them until they’re A-Rank or S-Rank. When all that has been accomplished, return to the Chocobo Ranch and breed them, using the Zeio Nut to get them in the mood… and with any luck you’ll get a Gold Chocobo!
This shimmering bird not only has the best racing stats (when properly fed, of course), but it can cross any terrain on the world map; oceans, rivers, mountains… which means you can now search for Round Island, an unmarked, forested island surrounded by mountains along the north-eastern edge of the map (see the included map), where you’ll find the fourth and final Materia Cave. Inside you can obtain the Knights of the Round Materia, the ultimate summoning spell in Final Fantasy VII.
After obtaining this game-breaking spell, feel free to race your Gold Chocobo as much as you wish; there are plenty of prizes you can earn doing this which are valuable in their own right, but you can also score massive amounts of GP… enough to fuel whatever battles you feel like doing in the Battle Square.