The first thing you will need to do after accepting the assassination quest from Elpenor is find a boat. Speak to the shipbuilder in Sami. Regardless of the dialogue options you choose, the shipbuilder will not sell you his boat for less than 100,000 drachmae. He does however provide some useful information in the form of an update on the Cyclops; he can be found in Kleptous Bay, and so can his ship.
When you are approaching the bay, use Ikaros to examine the situation. Take note of the amount of opponents, and the precise location of the Cyclops. You can then move through the camp and eliminate opponents in whatever way you see fit. When you approach the Cyclops a cut scene will initiate, after which you will be thrown into the midst of battle.
Speaking with the ship captain Barnabas will lead you not only to a ship, but a crew and captain to go with it. Meet him in Sami Harbor to inspect your new ship. After speaking with him and saying farewell to Phoibe and Markos, a cut scene will follow and the quest will complete.