"A group of smugglers pillaging ancient caves is being led by a Templar aristocrat. Find their group and kill him."
This contract cannot be completed until you have obtained the Diving Bell in Sequence 6, Diving For Medicines. Be sure to also acquire a dagger from a Scout anywhere in the world. It will make things a lot easier. You need to dive Ambergris Key.
Getting through Ambergris Key is not hard in terms of the cave. What makes it hard is all the Jellyfish and the urchins. Move around them carefully. The path to the temple is very straight forward.
When you make it out the water and find the ruins looming over you, you are in the right area. Look up to the Northwest. There is a sentry up there with a second pirate joining him at regular intervals. Wait until the patrolling pirates moves away. At that point, kill the other with the dagger. Climb up the nearby pillar and take up a corner position at the entrance of the temple. Wait for the patrolling pirate to come back toward you and take him down as he reaches the corner. Now grab the nearby musket and head into the main part of the temple. Use Eagle Vision to identify your target and then shoot him. Fight through the remaining forces and enjoy your victory.