Every so often you will encountered a pirate convoy while on the nautical map, either by sailing past it while it is in range or by having one directly attack one of your ships. When this happens you need to follow it (keep it in range) as it moves along the map. Eventually it will reach a point on the coast and disappear and a pirate nest will be revealed on your map. It is also a good idea to check a town’s palace as any pirate sightings made by other ships will be noted with a rough area of where it appeared. The sightings will include a town or area where the sighting was made. From there all you need to do is sail around the area until you locate the ship, then follow it as mentioned above.
You can also learn the location of pirate nests from the occasional person in a town’s tavern, but this will cost you a sum of gold that is scaled based on your overall rank. Also, if you are married, your spouse will occasionally inform you of a sighting similar to the stranger in the tavern but without the gold fee.
TIP: If you encounter a stranger in a tavern offering you gold in exchange for information on a pirate, save your game, pay the fee and learn the location, then reload to save the gold. The pirate nest will still be there. Also be aware that the tips are very vague and usually consist of “last seen off the coast of X,” so you may need to expand your search if you don’t find them in the immediate area.
NOTE: Although the achievement requires 10, some people have reported the achievement unlocking before or after 10 nests discovered, so if it doesn’t unlock, keep on the look out for more. There is no shortage of pirate nests as you progress through the game.