This is story related and cannot be missed. It is unlocked when you open a secret door on the far left side of the beach and enter it.
The door is revealed and unlocked when you hack away the vines with a machete, insert two gold medallions into their respective slots, and solve the vine puzzle.
The machete is in a rusty box that you dig up on the right side of the beach with a shovel obtained from the ground floor of the lighthouse. Take the box to the security level 2 room and shoot it open with the machine gun. The machete drops out of the opened box.
One of the medallions is in a chest at the top of the lighthouse opened with a skull key obtained from a diving helmet next to the chest. The other medallion is inside an artifact in basement 2. The artifact is opened by a key obtained from the box in security level 3 room. Five ornate gems must be affixed to the box to open it. The artifact in level 2 is raised by solving a puzzle. The key to the puzzle is inside the box opened by the club, spades, heart, & diamond keys. The box, which contains and ornate gem, is on a small table just outside the elevator in basement 1.
After hacking away the vines on the far left side of the beach with the machete and inserting the two medallions, they turn to uncover a puzzle. The vines in the puzzle must be connected. Start with the bottom hexagon. Turn this hexagon so the bottom right angle includes a spiked vine. The top of this hexagon will have two stems that will connect with vines in the hexagon just above them. Using this hexagon as a key, move in sequence around the outside of the puzzle making sure that all vines connect. Once you have the outer ring correct, do the same thing with the middle ring. Finally, turn the center piece so it correctly connects. As soon as the puzzle is solved, a previously hidden doorway will automatically open to the right. Enter this doorway to unlock the achievement.