Copy/Paste from original game, solution by General Arcane.
Narwhals can be found in the north-east of the North Atlantic. For this achievement, you simply need to harpoon one. Narwhals are more resilient than other sea creatures, and you may have difficulties killing one. I would suggest investing in one or both of the Harpoon strength and Harpoon storage upgrades for the Morrigan to make this process easier.
When you find one, enter the highlighted circle in the water and hold cn_B to begin the harpooning minigame. This involves spearing a narwhal and following it through an ice field, bracing (hold cn_X) when you approach some chunks of ice. While being towed by it, you need to hit it with more harpoons to bring down it's health and eventually kill it. This is where having the upgrades comes in useful.
It is likely that you will end up detaching from the narwhal at some point during the chase. When that happens, look around the water near the boat for a white patch - this is where the narwhal is about to surface. If it is very close, then it will launch into the boat and knock a bar of health away. What you want to do is try to time your throw so that your spear hits it just as it emerges from the water. Then repeat the chase and brace sequence once again. Equally, it can start a distance away and approach the boat and deal a lot of damage - in this case, listen for the sound of it breaching the water's surface.
The narwhal takes around 15 harpoons to kill, and the default that you start with is 20. Therefore, you can only afford the miss 5 shots, unless you invest in the upgrades.