In order to get Cid's final limit break, you need to unlock the six prior limit breaks and obtain the item that teaches Cid 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.
Cid's limit breaks
Stage 1: Boost Jump, Dynamite
Stage 2: Hyper Jump, Dragon
Stage 3: Dragon Dive, Big Brawl
Stage 4: Highwind
Unlock order:
Use Boost Jump 7 times in order to unlock Dynamite.
Get 60 kills with Cid in order to unlock Hyper Jump.
Use Hyper Jump 6 times in order to unlock Dragon.
Get 76 kills with Cid after unlocking Hyper Jump in order to unlock Dragon Dive.
Use Dragon Dive 5 times in order to unlock Big Brawl.
Use the Highwind item after unlocking the 6 previous limit breaks in order to unlock Highwind.
The Highwind item is located in the crashed Gelnika on the seabed floor and is only accessible via Submarine. It in a chest in a hallway on the left just past the room where you fight Rude and Reno.