Take the boat and cross over to Ithaka. When you are half way to the island use Ikaros to scout its key features and any potential opponents. You will also be able to identify the location of the shroud. With everything scouted, begin the infiltration of the palace and kill the enemies systematically with stealth assassinations and ranged shots.
Note: If you would rather take a more direct approach in taking care of the thugs, you will find the quest marker for 'A Small Odyssey' nearby. Go to it and open the cage, within which is Odessa. She will ask you to help her fight to the palace. In return you not only have the assistance of her fighting skills; you can also begin a romantic fling with her, leading to further quests in pursuit of romance.
If you would prefer to kill as few enemies as possible, you can go directly to the captain of the company and assassinate him. The shroud can be found on his person. Once you have it, return to Elpenor who can now be found at the Temple of Zeus, near Sami, to complete the quest.
Note: When you return to Elpenor he will ask you to accept an assassination mission. While the dialogue options may seem to provide the option to refuse, it is impossible to do so. Regardless of your choices, the dialogue will end in you accepting the quest.