Get in your sub and ride it to the docking area near the Gold Saucer desert.
Dive under water and there should be an underwater passage right in front of
you. When you pass through and surface you'll be in a small area of water
beside a waterfall. Dock on the side and walk into the waterfall. Make sure
you have Vincent in your party. When you enter, watch the scene.
Note that you can also reach this area via any mountain climbing Chocobo.
Once the scene is over leave the area and continue with the game, main story
or leveling or anything. After a certain amount of time has passed (couple
hours is a good estimate, though I'm not exactly sure what the requirements
are, return to the waterfall with Vincent and examine the glowing pedestal to
receive Death Penalty and Chaos, his final weapon and level 4 limit break.