To learn level 4 Limit Breaks, you must have learned all of that character's other breaks. Furthermore, you must have a special manual (you can tell what it is since it has the same name as the Limit Break). If you try to use the manual on another character, or on a character who has yet to learn all his or her breaks, you'll get a message in red and white. But when you have filled all the requirements, simply using the manual on the correct person will automatically give them their last Break. Here are the locations of each character's manual:
CLOUD STRIFE You must earn 32,000 battle points at the Gold Saucer in one visit. You can then trade them in for the manual. BARETT WALLACE Get it from a lady wearing a hat in one of the buildings in North Corel after the train ride in Disc 2. TIFA ROCKHEART Go to Nivelheim and play the 'Highwind' theme on the piano in Tifa's house. Either one will work. Tifa must be in the party. X, S, T, L1+T, L1+S, X, S, T, L1+X, O, X, S, X or D, L, U, L1+T, L1+S, D, L, U, L1+X, R, D, L, D AERIS GAINSBOROUGH Get 1xx wins in battle (where xx are two matching digits). Then go to the cave where the sleeping man is and he'll give you the Mithril. Head to the blacksmith's house by the Gold Saucer, give him the Mithril, then climb up the stairs and examine the metal lid at the end of the walkway. Once you get the Highwind, doing this is a snap. But Aeris will have already left you by then. So, to get her manual while she's still in your party in Disc 1, do the following: Hop on the Gold Saucer Buggy. If you haven't gotten it yet, keep playing until you've finished the Gold Saucer area. Then pilot the Buggy into Costa Del Sol. You'll enter the town as if you had walked into it. Go to the harbor and talk to the sailor by the boat. Choose the top option to pay 100 gil and you can then walk along the dock and enter a ship, which will return to Junon Town. Although there's not much new here, you will get a different reaction from most people because you're no longer dressed up as a guard. Anyway, once you exit the city (the fastest way is to take the helicopter), you'll find that you've brought the Buggy with you! From here, it's a simple matter of heading towards the river, crossing it at the ford below the waterfall, then heading up to the cave where the sleeping man is. And after getting the Mithril, you have to go all the way back to the Eastern Continent so you can reach the blacksmith's house. RED XIII Go to Nivelheim and unlock the safe in the right wing of Sephiroth's Mansion. You'll receive Red 13's manual from the boss when you defeat him. YUFFIE KISARAGI Return to Uutai after completing Yuffie's sub-quest. Head to the pagoda and beat the five bosses within--she'll get her manual once Godo is defeated in battle. VINCENT VALENTINE Once you have the submarine or a Green, Black, or Gold Chocobo, go to the waterfall in the middle of the Western Continent. If you enter the waterfall from the left side with Vincent in your party, he'll meet a girl from his past (Lucrecia). You have to visit the falls twice, once during Disc 2 and again in Disc 3; it's during your second visit that you'll get his manual. CID HIGHWIND After you get a submarine, go underwater and search for the wrecked plane near the southern part of the World Map, between the Western and Eastern continents. His manual is in one of the treasure chests inside the plane. - Note that Cait Sith only has two Limit Breaks; his inital one and one for Level 2. You still learn it the normal way you'd learn the first break of a new level. The same applies to Vincent, who has four Break levels but only one break per level. All other characters have two breaks a level (but only one break for Level 4).
Limit Breaks become stronger and stronger as you play. This is due in part to your character's current level. Limit breaks that inflict damage become stronger depending on your Attack Power as well, even ones like Cait's Dice attack (in which the damage amount can vary), and Vincent's transformations (even though he doesn't use his guns). At the very least, equipping a strong weapon will add to the basic amount of damage a Limit Break can inflict*. * The only exception to this is Cait's Slot attack, when he summons a monster; damage is determined normally for this attack. Remember, if the Break doesn't inflict damage, it isn't affected by your character's Attack Power.