The first mission can be started by speaking with the assassin in central Nassau. Once the mission begins, run across the nearby marketplace and find the persons of interest marked with the orange objective markers.
We want to eavesdrop on these fellows. Follow them down the street to the west of the market using the crowds, benches and market stalls as cover from detection. When they head west away from the market and down the hill, hop up on the rooftops to the right of the road and tail them from above. When they enter a small alleyway the tailing section will be complete.
Head over to the far side of the roof overlooking the open area below and use Eagle Vision to identify the new target. Use the tree at the northern end of the roof and follow its branches to the end. From here, look below and wait for the target to pass beneath us. When he does, highlight him and perform an air assassination to end the mission.