This Quest There Can Be Only One can be started serval ways, but also by just visiting the small Island in the middle of Lake.
To complete the Quest (Embodiment of the Five Virtues Achievement) you need to display the five chivalric virtues during your stay in Toussaint: Compassion, Generosity, Honor, Valor, and Wisdom. If you already completed a few Quests it’s possible that you already have completed a few virtues, but it’s possible that you can’t complete the Quest since you chose the wrong options. Here is a (work in progress) List of Oppurutnies where you can earn the virtues:
– Main Quest: The Beast of Toussaint – After fighting the Shalemaar in the arena decide to spare its life.
– Side Quest: Mutual of Beauclair’s Wild Kingdom – Decide not to kill the silver basilisk
– Contract: Big Game Hunter – After helping Beledar, agree to visit him at his feast. Wait until noon the next day, then head on over to the picnic. Ask about his daughter once the opportunity presents itself.
– Go to Main Square of Beauclair and a child will deliver a letter to you. Give him 5 crowns for his trouble.
– The Warble of a Smitten KnightSide Quest: The Warble of a Smitten Knight – After the horse race choose to accept the mounted duel against the prince and win it.
– Side Quest: Goodness, Gracious! Great Balls of Granite!
– Side Quest: The Warble of a Smitten Knight – After following the girl into the woods and returning to camp, decide to finish the tourney and win.
– Side Quest: Mutual of Beauclair’s Wild Kingdom – Turn down the extra gold at the end.
– Main Quest: La Cage Au Fou – Thoroughly exploring the Wight’s Lair and when hiding in the closet try to lift the curse instead of attacking.
– Side Quest: Gwent: To Everything – Turn, Turn, Tournament! – Win the tournament.
If you have completed the five virtues go back to the Lake to complete the Quest, after that you receive the Aerondight Sword and the Achievement
thanks to @dabomb3112 from xboxachievements.com