Swim to Vaas' island and infiltrate the compoound. Continue inside until Vaas sets the building on fire. Make your way out and to the waiting pirates outside. Quickly leave the rooftop and head to the building to the left to get enough cover and take out the pirates more effectively. Fight through the compound until you reach the next building.
After the scene, you'll be in another sequence. Keep walking until you reach Vaas then shoot him. In the next sequence, keep pushing forward and keep destroying Vaas's apparitions until you reach the objective point. Perform a takedown to defeat Vaas and complete the mission.
Leave the temple for a scene.