Most of the animals in Assassin's Creed 4: Black Flag are easy enough to find and kill. As for the White Whale, that takes a bit of luck. You also have to know where to look. Having trouble? Don't worry, because thar she blows!
Ahem, anyway, you can only find the white whale during an AC4 Community Event, of which, there are three: social chests, royal convoys and drum roll please, white whales. If you come close to accessing one of these events, the corresponding icon will appear on your screen. On top of that, it will be shared with your AC4-playing friends; a White Whale may appear anywhere within the Caribbean.
Track down and subsequently harpoon a White Whale, and you'll receive a White Whale Skin. You'll need three of these skins to craft the Whaler Outfit. The Sell Price for the White Whale Skin is 4,000R, while the Buy Price is 20,000R.