To begin this quest you must speak with Brasidas, who can be found overlooking the docks at Amphipolis. Speak with him to see what he has to say. If you refused his advice during the quests 'Monger Down' and 'Judge, Jury, Executioner', he will not be very amiable since you tarnished his reputation. Aside from dialogue, this will not inflence the structure of the quest. When you are ready, follow him into battle. You will first have to defeat a group of Athenians at the nearby scaffolding. With the assistance of Brasidas and the other Spartans, this will not be difficult. Focus on the archers initially to minimise losses, and be careful not to use too many AoE attacks as this may harm your allies unnecessarily. When the Athenians are dead, head east to the beach where the main battle is taking place.
The battle will at first play out like any ordinary conquest battle. Defeat as many captains as possible before the point at which a mercenary usually arrives. As with last time, your sibling will arrive at this point and a cut scene will follow in which Brasidas is tragically killed. Just before you can engage in battle with your sibling, Kleon will shoot them in the back and then run away. You must now chase Kleon and confront him alone on the beach. Despite his status, he is not a particularly tough opponent to defeat; he has no heavy defence and no special skills. You can bring him down with a combination of heavy and light attacks, but use your special skills if you want to make it quick. When his health bar is completely depleted a cut scene will initiate. You now have to decide whether to kill him swiftly or slowly. There are no real consequences to your decision. When the deed is done, the quest will end.