During naval battles enemy sailors will fall overboard as you attack their ships. You can rescue those sailors by bringing your ship close to them. They are often difficult to see unless you have the camera zoomed in but can usually be found around the sharks that will gather as the battle continues.
You will probably rescue most without realizing as you manoeuvre around the naval battle map. A good tactic is to wait until the enemy has lost all but 1 ship, and while your AI partners chase it down, you focus on rescuing sailors. This will most likely come naturally as you play through the Adventurer campaign or as you work toward the other achievements.
TIP: If you are struggling with this achievement, attack a pirate hideout with a strong convoy and let the AI do the attacking as you hold back and focus on rescuing sailors. As long as you only attack the pirate convoys and not the hideout, the convoys will respawn after 10-20 minutes.