Unlike other characters, Aerith's final limit is missable. Make this a priority after getting the Tiny Bronco, because once you finish the Temple of the Ancients, you must use an earlier save or a new file.BASICS OF LIMIT BREAKS
To get Great Gospel, you need to take the Buggy back to Junon. Drive it back and into Costa del Sol, then take the Cargo Ship back to Junon. Drive the buggy north of Junon to find a river to drive over. There is a cave here with a man sleeping inside. He will only wake up if the last two digits in your number of battles fought are the same, i.e. 77, 144, 255. When he does, he will either give you a Bolt Ring or Mythril. If he gives you the Bolt Ring, fight more battles until the digits are the same again, as he should give you the Mythril the second time.
Once you have that, take the Tiny Bronco to the southeastern edge of the western continent, east of Gongaga, to a house on the coast. This is the Arms Dealer. When talking to the man inside, if the conversation is on the Keystone, choose to talk about something else, then give him the Mythril. Once he lets you take a box, go upstairs and around to the small safe; Great Gospel is in this safe. Use it on Aerith to get the achievement.