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In order to get Cloud's final limit break, you need to unlock the six prior limit breaks and obtain the item that teaches Cloud his final limit break. The way to unlock each limit break differs for each character but are essentially similar. You unlock the second limit of each stage by using the first limit of that stage a bunch of times, and you unlock the next stage by getting a certain number of kills.

Cloud's limit breaks:
Stage 1: Braver, Cross-Slash
Stage 2: Blade Beam, Climhazzard
Stage 3: Meteorain, Finishing Touch
Stage 4: Omnislash

Unlock order:
Use Braver 8 times to unlock Cross-Slash.
Get 120 kills with Cloud in order to unlock Blade Beam.
Use Blade Beam 7 times in order to unlock Climhazzard.
Get 200 kills with Cloud after unlocking Blade Beam in order to unlock Meteorain.
Use Meteorain 6 times times in order to unlock Finishing Touch.
Use the Omnislash item after learning the six previous limits in order to unlock Omnislash.

The Omnislash item is obtainable in the Battle Arena in the Gold Saucer. You need to rack up enough BP in order to purchase it from the Battle Arena. Prior to unlocking the Highwind it costs 51,200BP, but, once you have the Highwind, the price is reduced to 32,000BP. Given that you also need 64,000BP to purchase the W-Summon materia, you may wish to wait until you have the Highwind before purchasing Omnislash.

Of course, it costs 10 GP per battle in the Battle Square. The best way to gain GP is chocobo racing. The battles are made tough as you receive a random 'handicap' each round, inflicting some penalty on you. Status effects can be counteracted by equipping the Ribbon accessory, however. Moreover, if you die, then you get 0 BP, and you lose all your BP every time you leave the Battle Square.

So, not only do you need a superlatively tough character, but you need a large amount of GP in order for you to enter the battle arena enough times in one pop to get enough BP. It really is luck how well you do, and sometimes backing out whilst you are ahead is recommended. Out of all final limit breaks, Omnislash takes the longest to get, and for good reason as, if Cloud is a high enough level, it can inflict more damage than Knights of the Round.