Level 4 Limit Breaks:
In order to learn each of the characters Level 4 Limit Breaks you will have to obtain an item in game that is capable of teaching the character how to do the move. You'll also have to learn all of the characters Level 1, 2 and 3 Limit Breaks, which can be a challenge for some characters. For information on how to learn new limit breaks click here.
You can obtain Omnislash by spending 32,000 battle points on it in the Battle Square of Gold Saucer. For information on how the Battle Square mini-games work click here.
Final Heaven (Tifa)
A return trip to Nibelhiem, Tifa's home town, and a little bit of piano know-how will get you Tifa's Level 4 Limit Break: Final Heaven. For more information about doing this correctly click here.
Most players will obtain this Level 4 Limit Break without even trying, which is a good thing because you can't go back to get it. Obtaining Catastrophe requires you to successfully stop the train on Mount Corel that's barrelling towards North Corel (click here for information on this part of the game). If you managed to do it successfully then head to the upper area of North Corel and go inside the Inn. Talk to the woman inside to receive your prize.
Cosmo Memory (Red XIII)
Cosmo Memory is another really easy Level 4 Limit Break to find. Go to Nibelheim and complete the side-quest to earn Vincent as a playable character. When you open the safe to recieve the key you'll also receive Cosmo Memory and the Odin Materia. For more information on obtianing Vincent one of the secret characters click here.
Cid's Level 4 Limit Break can be found on the Sunken Gelnika which you can make your way to at any time once you gain access to the submarine. The enemies inside it can be a little rough early on in the game, so save before you go venturing too deep. More information on the treasures found on the Sunken Gelnika can be found by clicking here.
Cait Sith has no Level 4 Limit Break.
All Creation (Yuffie)
Yuffie's Level 4 Limit Break is obtained during a side-quest in Wutai, Yuffie's home town. Doing this side-quest before disc 3 means that you're going to have all of your Materia stolen by Yuffie. Click here for instructions on how to get your Materia back from her. After all that pointless work (or if you're on disc 3 and Yuffie no longer steals your Materia) click here to read up on how to complete Yuffies side-quest in Wutai.
Put Vincent in your party and jump in the submarine. Stay on the surface and look for a river just north of Costa del Sol. Ride it all the way up into the mountains until you reach a crater-like area surrounded by mountains and then hop off the sub. You can now venture in behind the waterfall into a cave. Once inside Vincent will have a flashback (assuming he's in your party) related to his former lover. Once its over you will need to fight 10 battles and then return to the cave. After ten battles returning to the cave will get you both his Level 4 Limit Break, Chaos, and his ultimate weapon, Death Penalty.