Go get the buggy from by Nibelheim and drive it to Costa Del Sol, then drive it right into town (don't get out of the buggy). Then talk to the guy by the boat to ride back to Junon, leave Junon and you have the Buggy on the first continent. Ride it over the shallow part of the river to reach the cave. When the last 2 digits of the number of battles you've fought are the same odd number (or was it even?) the guy inside will give you a mithril. (this can actually be done anytime after you get the buggy).
Then after Rocket Town go to the lone house on the world map near Gongaga and give the guy inside the mithril and open the small box upstairs (looks like a safe in the wall) to get her limit manual.
Then it's just a matter of her learning all 6 of her other limits and then using the manual on her.
--- http://www.geekologie.com/2008/08/25/ninja.jpg Everytime you see him, the phiefer's just so hype. He's dope on the board and he's magic on the mic. ~fidormula
Without any grinding (albeit with biasing kills in Aeris' favour), I was able to teach her the limit break as soon as I got it, having all 6 of her limits a little bit before Rocket Town. This required having her in the party at all times, and letting her kill the majority of the enemies (though not technically all of them). Putting her in the front row with cover to get her 2-3 and 3-3 limits more quickly helps out, too. --- Now playing: Pokemon Red (Black/White), The Beatles: Rock Band, Earthbound (1.5x enemy stats/hard mode hack)