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In order to get Vincent's final limit break, you need to unlock the three prior limit breaks and obtain the item that teaches Vincent his final limit break. Since Vincent only has four limit breaks he only acquires new ones by getting a certain number of kills.

Vincent's limit breaks:
Stage 1: Galian Beast
Stage 2: Death Gigas
Stage 3: Hellmasker
Stage 4: Chaos

Unlock order:
Get 40 kills with Vincent in order to unlock Death Gigas.
Get 56 kills with Vincent after unlocking Death Gigas in order to unlock Hellmasker.
Use the Chaos item after unlocking all 3 previous limit breaks.

The Chaos item is a bit hard to find if you don't know where to look for it. There is a cave near Nibelheim that is only accessible via Submarine or via Green, Black, or Gold chocobo. Enter the cave and you will find Lucrecia. After the scene, leave and fight 10 random encounters. Once this has been done, return to find the Chaos item.