Level 4 limits are the charcters best limit breaks. Every character has them except Cait Sith whose only goes up to two. To learn these you must have all other limits mastered to level 3, and then use an item.To get these items:

CLOUD
At the Battle Square, buy Cloud's OmniSlash for 32,000 points.

TIFA
On the piano in Tifa's house in Nibelheim, play the following keys (T=Triangle S=Square) X, S, T, O, X, S, R1+L1+T, R1+L1+S, X, S, T, R1+L1+X, O, X, S, X. Play this 2 times ina row, and press start. If done properly you will recieve Final Heaven.

AERIS
In the cave southeast of Midgar their is a sleeping man. Talk to him. Sometimes he tells you how many battles you've fought. Talk to him when the last two digits of this number are the same and you will recieve the mithril. In the Weapon Seller's house, give him the metal to open a box. The small one contains the Great Gospel.

BARRET
In disk 3 talk to the lady in North Corel who is in the barrack's. She will give you Catastrophe.

RED XIII
Open the safe in Nibelheim (see how to get vincent) and you will get Cosmo Memory.

YUFFIE
Beat all the Pagoda Bosses in Wu-tai to get All Creation.

CID In the Gold Saucer, get 5,00 points in the Laser game to get the Flayer, Cid's best weapon. Better than the Venus Gospel, and it has a normal Materia growth to!

VINCENT
You get Chaos with The Death Penalty. (See Ultimate Weapons)