Edward Kenway isn't just a badass, he's a stylish badass. You expect him to strike fear to the hearts of others in just a single outfit? No way, he needs a whole Captain's cabin full of outfits.
Here is a full comprehensive list of the singleplayer outfits in the game that you can either acquire by playing past Assassin's Creed games, purchasing them from vendors, or crafting them with various animal hides.
Outfits from past Assassin's Creed games
Altaïr Ibn-La’Ahad Outfit – You can unlock this by having any existing data on your system from a previous Assassin’s Creed game.
Ezio Auditore Outfit – You can unlock this by having any existing data on your system from two previous Assassin’s Creed games.
Connor Kenway Outfit – You can unlock this by having any existing data on your system from three previous Assassin’s Creed games.
Outfits acquired through UPlay
Edward The Legend Outfit – You can unlock it for 20 UPlay Points.
The Vengeful Daughter Pack – You can unlock it for 40 UPlay Points.
The Blades of Toledo Pack – You can unlock it for 30 UPlay Points.
Outfits you can purchase
Brown Cloak – You can purchase it from the general store.
Crimson Cloak Outfit – You can purchase it from the general store.
Merchant Outfit – You can purchase it from the general store.
Pirate Captain Outfit – You can purchase it from the general store.
Pirate Cloak – You can purchase it from the general store.
Politician Outfit – You can purchase it from the general store.
Privateer Outfit – You can purchase it from the general store.
Outfits you need to craft
Cat Outfit – You can craft this by purchasing the animal pelts from any general store, or hunt for them.
Explorer Outfit – You can unlock this by completing Community Challenge #6.
Feline Pelt Outfit – You can craft this by purchasing 1 ocelot pelt and 1 jaguar pelt from any general store, or hunt the respective animals.
Governor Outfit – You can unlock this by finding a Social Treasure Chest.
Hunter Outfit – You can craft this by purchasing the red howler monkey skin and white jaguar pelt from any general store, or hunt for the animal.
Mayan Outfit – You can unlock this by collecting 16 Mayan Stones from each of the Mayan Stelae missions and then opening up the secret door in Tulum; which unlocks after Sequence 4.
Officer Outfit – You can unlock this by completing the “Gibraltar” Mission in Kenway’s Fleet.
Shark-Hunter Outfit – You can craft this by purchasing 1 Bull Shark skin and 1 Hammerhead Shark bone from any general store, or hunt for them with your Rowboat and harpoon.
Stealth Outfit – You can unlock this by completing half of the Assassin Contracts.
Templar Outfit – You can unlock this by collecting 16 keys from each of the Templar Hunt missions and then opening up the cage in the Great Inagua hideout.
Whaler Outfit – You can craft this by purchasing 3 White Whale skins from any general store, or hunt the whale with your Rowboat and harpoon.