Cid learns Big Brawl after using Dragon Dive five times. Good ways to get him to use his Limit more often is to inflict Cid with Fury and equip him with Cover and/or HP↔MP so he can take more damage during battles. Enemies that deal fractional damage are also good for raising the party's Limit gauge, such as the Valron that appears in the Nibel and Rocket Launch Pad Areas.
Big Brawl deals more damage than Cid's preceding Dragon Dive, but has no chance for inflicting Instant Death like the latter. It is still usually preferable over Dragon Dive, as it hits more times, dealing overall more damage. It is Cid's best Limit Break until he obtains the manual for his ultimate Limit, the Highwind.