If desired, get harpoon upgrades, harpoon storage, strength, and extra armor to make this process easier. Sail to a Killer Whale hunting location (for example, coordinates 537, 340 on the world map). After a deck hand announces the presence of a whale, Kenway will be sent with a harpoon to hunt it. Harpoon the whale and follow it, being careful when it dives. It will eventually surface again on the horizon and run at your boat. Harpoon it again to avoid taking damage. Repeat the process until the whale's health is taken down to unlock the achievement.