After accepting the contract, if you look at the map whilst in the Arroyos zone, you will notice that there are two small, restricted areas: one at the marketplace in the centre of town and the other at the dock. Once you begin the contract, move to the marketplace and use Eagle Vision to tag your target.
A brief conversation between the target and a merchant will ensue before the target runs off and gets on his ship. Run over and jump on the Jackdaw as fast as you can, get behind the wheel and begin your pursuit so that he is unable to escape.
Chase him down, destroy his ship and then board it. Kill him to complete the contract. Feel free to finish boarding the ship afterwards!