"Redingote Up!" Go to a General Store and select the "Hunting Goods" tab. Buy the Red Howler Monkey Skin for 5,000 R and White Jaguar Pelt for 6,000 R. Select the "Crafting" tab at the main menu, then select the "Hunting Outfit" option.
"Killer Killer" Sail to a Killer Whale hunting location (such as coordinates 537, 340 on the world map). After a deck hand announces that there is 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 or trophy. Note: Get harpoon upgrades, harpoon storage, strength, and extra armor to make this process easier.
"Excavator" To find a buried treasure, first obtain a treasure map. An easy one is found on Mariguana Island, at the coordinates 878, 539. Collect the map to see a picture and the coordinates of a treasure. This particular treasure can be found on Andreas Island, at the coordinates 575, 717. To unlock the locations of other treasure maps, you can talk to the barkeepers of taverns, or just explore the world and synchronize viewpoints.
"Hungover" Repeatedly drink at a tavern until you pass out. A tavern can be found in Nassau, which is one of the first locations you will visit during the main story. Walk up to the bar, and interact with the bottle to start drinking. You have to drink at least five times to pass out.
"Silence, Fool!" Go to any warehouse found at farms. They have a restricted area around them (shown as red on the world map) and are marked on your map if you synchronize viewpoints. One can be found in Nassau, at coordinates 633, 784. Once you enter the restricted area, there will be an alarm bell on your HUD. Then, get noticed by an enemy and wait for him to ring the bell. Kill him fast with a melee attack when he starts ringing the bell to unlock the achievement/trophy. Note: You can also do this at warehouses that have already been looted. The enemies will respawn after a while.
"Siren Song" To rescue pirate hostages by distracting enemies with dancers, you have to allow some of your crew members to die. Board an enemy ship and your crew should start fighting. Many of your crew will probably die. Then, go to Kingston and go to coordinates 623, 172. There is a restricted area where two enemies are aiming at captured pirates. You can hire some dancers nearby, just up the street. Send the dancers to these two enemies. When they are distracted, sneak behind them and free the pirates to get the "Siren Song" achievement/trophy. If this event does not appear (even after losing many of your own crew members), fast travel to another island, and return later.
"Wild West Indies" First, craft all pistol holsters. You can purchase the required crafting items from any general store (so you do not have to hunt down the animals on your own), if preferred. Also, purchase and equip the "Cannon-Barrel Pistol" for one-shot kills. Once done, find a group of at least four enemies, walk up to them with the pistols selected in your weapon wheel, and press Y without manually aiming to have each shot kill an enemy and get the "Wild West Indies" achievement/trophy.
"Owned" You can complete every activity on "Florida" island, located at coordinates 409, 815. When you scroll over an island on the world map, you can see which activities it has to offer. Normally it offers some collectibles and viewpoints. Florida island has very few activities to complete so synchronize the viewpoint, collect the two animus fragments, open the treasure chest, and pick up the bottle message to get the "Owned".