Cloud's Ultimate Weapon is called Ultima Weapon, and to get it you must defeat Ultimate Weapon (I don't know if Square did this on purpose or not). On Disc 3 you'll find Ultimate Weapon hovering over a lake near Junon. Just fly up and hit him to enter the battle. After a little while he'll fly away; just chase him until he stops again. Once he's finally defeated you'll get Ultima Weapon as a reward!
You can get Cloud's Level 4 Limit Break, called Omnislash,
by earning 32,000 battle points at the Battle Arena in Gold Saucer. Whatever
you do, don't leave the Battle Arena until you have it because you'll lose
all your battle points the second you step through the door! So be sure
to have tons of GP because it's 10 GP per fight. You must have reached
the Level 3 Limit Break before Level 4 can be applied.
You can get Barret's Level 4 Limit Break, Catastrophe,
by going back to North Corel after Meteor has been summoned. Talk to the
woman in the house on the west side and she'll simply give it to you.
Aeris's Level 4 Limit Break is a little tricky. East of
Junon, if you have a blue or gold chocobo you'll find a cave with a sleeping
man inside. Talk to him and he'll tell you how many battles you've fought.
If the last two numbers match (example, 244), he'll give you an item. This
only works once so it kind of sucks. If he gives you a piece of Mythril,
you can take it to the Weapon Seller near Gongaga to receive Aeris's Great
Gospel.
Cait Sith's Limits only
go to Level 2!