In order to teach Aeris her final limit break, you need her to have learned all six prior limit breaks, and the item that teaches Aeris her final limit break. The way learning new limit breaks differs for each character, but are fairly similar. In order to get the second limit break for any given stage, you just need to use the first one a bunch of times, but, in order to unlock the next stage, you need a specific number of kills.
Aeris' limit breaks:
Stage 1: Healing Wind, Seal Evil
Stage 2: Breath of the Earth, Fury Brand
Stage 3: Planet Protector, Pulse of Life
Stage 4: Great Gospel
Unlock conditions:
Use Healing Wind 8 times to unlock Seal Evil
Get 80 kills with Aeris to unlock Breath of the Earth
Use Breath of the Earth 6 times to unlock Fury Brand
Get 80 kills after unlocking Breath of the Earth to unlock Planet Protector
Use Planet Protector 5 times to unlock Pulse of Life
Use the Great Gospel item after unlocking all 6 previous limit break to unlock Great Gospel
In order to obtain the Great Gospel item, you need to give the weapon dealer who lives near the Gold Saucer and Gongaga a piece of mithril, and then make sure to open the small box on the top floor of his house. He won't be there, however, until after you have escaped Rocket Town in the Tiny Bronco. The only thing left is getting some Mithril.
The only way to get Mithril is from a sleeping old man in a cave near Fort Condor and the Mithril Mines, however, you can't get there on foot. Once you have obtained the buggy from Gold Saucer, return back to Costa del Sol and then talk to the sailor in front of the ship to be taken back to Junon.
Upon leaving Junon you will be in the Buggy, which you can use to cross the shallow river to get to the cave. What the sleeping old man will tell you is random, so keep leaving and entering until he tells you how many battles you have fought. If the last two digits are the same and are odd, then he will give you a piece of Mithril.