Chocobo Ranch

Head east and south to reach the Chocobo Ranch. Talk to the chocobo at the fence and answer "Wark". The chocobos will do a dance and you'll receive a Choco/Mog. Head to the barn in the back and talk to Billy to find out how to catch a Chocobo. When ready to go, answer "Not Interested" and then buy a Chocobo Lure and some greens (Krakka Greens are probably the best choice at this point).

Wander around the ranch until you enter a battle with a chocobo in it. Feed the chocobo some greens to keep it from running and kill all other enemies, being careful not to hit the chocobo. Afterward, you'll capture the chocobo and be able to ride it. Head south and west, avoiding the shadow of the Midgar Zolom (if you don't you'll have to fight it) in the swamp until you reach the Mythril Mine. Dismount the chocobo and head towards the cave entrance. Just before entering, you'll find an impaled Zolom. Just keep going forward to exit and then enter the cave.

Obtain: Enemies: