Port Royale 4

If your this far into the game and want to know how to do this here is the fastest method I found, it isn't hard just time consuming. Wasn't the last achievement I got for the game but was the one I sunk the most in game resources and deliberate time into very late game.

Have three or four harbours pumping out tens and tens of Spanish galleons, too do this get a shipwright and park a galleon at the port. You can now make them with a large shipyard. You will need over 600 since for every 5 vessels you sink in an auto battle you will lose 3 of your own minimum.

Galleons take up only one captain command point so you can have eight in a captains fleet. This is better than having 3 "war galleons" that take up 2 command points each and 2 regular galleons since they take longer too make than just a regular one.

Get about five or six captains with the carpenter skill so they regenerate 70% health after a battle, give each 8 galleons and start attacking anyone your at war with, after they battle immediately return the post battle captain to your ports to repair and get 8 galleons total then return to attacking

You will sink 5 enemy ships per automatic battle and you will lose at minimum 3 galleons, this means you need multiple fleets throwing themselves at the enemy every time you buy a Letter Of Marque, which costs millions by the time you are late game and have a billion or more.

200 auto battles where you sink 5 vessels will get you the achievement. You can see how many ships you have sunk under the company hud information.

If anyone can tell me the better way too do this I'll rewrite giving credit too the individual.