After accepting the contract, if you look at the map whilst in the Grand Cayman area, you will notice that there is a small, restricted area in the northeast corner of the settlement. Once you begin the contract, there will be two assassination targets located inside this restricted area.
You can easily sneak in from the north over to the top of the buildings and perform an air assassination on the first target that’ll be standing in the centre of the area directly below you.
Doing this however, will spook the other target nearby and he will run off. Follow him across town and down the docks. Once you have him cornered, assassinate away. This will complete the contract.