The questline starts on Kythera Island (All the way south, a little west off center. South of Lakonis.). You'll come accros an upset group of worshipers harassing a man in front of a statue (In the northern part of the island if I remember correctly). Talk to the man and you'll start the questline "A God Among Men". You'll have to free someone (Empedokles) from a nearby fort and escort him back. Continue his follow-up quests until he asks you to get a disc from someone wearing purple. When I did this the man was passing nearby but he may walk a patrol route. Use your eagle to find him. Return with the disc and he says he'll meet you in the Cave of the Forgotten Isle - Thisvi - You've probably visited this isle much earlier on. It's just off the coast of Phokis. If you've already visited the Tomb within the Isle you'll have a fast travel point there. Once you meet Empedokles he'll ask you to open the door and then he'll lead you to the chamber beyond before swiftly being sent on his way, leaving you with a boss fight.
You'll probably want to be about level 35+ to start the questline and when tackling the cyclops you're probably going to want to be level 38 - 40.
There are 2 phases to the fight.
In the first phase, when at range, he will charge you while covering his eye and swinging wildly. When he does this put an arrow into his legs and he'll fall over, opening up an attack opportunity. He'll also smash and stomp the floor when at range, causing the roof to collapse around you. Simply keep moving to the side. Shoot him in the eye when he's not covering it for big damage crits. When close, dart in for some hits, then dodge away and move to range again.
When the second phase starts he'll grab a makeshift club and be a little more aggressive. Keep the same tactics (moving when the roof starts falling, shooting his eye when you can). He still occasionally stumbles when charging but it seems to be less reliable than before so be prepared to dodge a little more. Also be more carefull when in melee as the swinging club does a lot of damage.
Overall you probably want quick weapons. Hit him in the butt and dodge out the way to stop him hitting you or grabbing you. Remember to switch to death arrows (or special arrows if you use them).
Drop armour with assassin damage boosts and buff out your hunter and warrior damage for the fight (unless you're going to use assassin skill,obviously, but you're not going to get assassination attempts in on him).
It's not a terribly difficult fight once you have the patterns down.