Here's how I got it:
Map: Archipelago
Difficulty: Immortal (Deity also works)
Era: Information
Game pace: Marathon (Information era only gives 100 turns otherwise)
Opponent: Venice (Enrico Dandolo) / Duel
Victory types: Remove all
Barbarians: Your choice
City-states: Your choice
The opposing NPC will always send fleets to attack you on this difficulty no matter what you do, so focus on building yourself a large fleet. Keep in mind you need happiness and gold to maintain a huge army and a war.
- Found your 3 cities with walls and Mobile Sams garrisoned
- Pick Autocracy and start with Elite Forces, Mobilization, and Nationalism to reduce the amount of gold you spend on unit upgrades and maintenance
- Rush a fleet of Nuclear Submarines (Strongest) and Missile Cruisers. Destroyers are okay, but I would only use them to capture a coastal city, which is really unnecessary for this achievement.
** Optional: if you kept city states, you can use them to increase happiness and gold, but Dandolo will always poach them cause he can't found cities. **
At some point after you meet Dandolo, his fleet will appear near one of your cities. Surround his units with your fleet and save the game as "1" (or whatever you like). Start the war, destroy the entire fleet. There may be a contingent on each of your cities. Sink them all and save your game as "2."
Go back to save 1 and start the war again. Once it's done, save it on 2. Rinse and repeat till you get the achievement.
The reason I saved two files was to make sure the game updates the count. I could be wrong about how the game counts, and you may not need that second save, but that's just a precaution I opted to take. Commenters, feel free to dispel my little bit of count paranoia if it's unwarranted.