Although the achievement description says alone, this can be done in co-op, but it has to be you who find the secrets.
You can do it on any mission but it's easiest to do in Port Royal (Film 1, Chapter 1). To activate the compass you need to be controlling one of the versions of Jack Sparrow and then hold to turn it on.
Start in the prison, looking for the item, on the 6 o'clock position. Then continue to the first beach to find the planks, a pole (build it to reach a very elusive minikit) and the conch. Then move on to the hidden area that opens up after destroying the silver barricade in the big square next to the docks and look for the sausage, the golden sword and the fish in this backyard. Lastly, head to the second beach and use the cursed version of Jack to find the small crab underwater. Ride it to count toward "Sea turtles, mate".