To obtain this achievement you will need to have progressed through some of the main story missions without ever doing Kurt's companion quests. This is so Kurt's friendship level with you is set to Suspicious. When you return to Constantin to inform him that the previous settlers on the island were part of the Merchant Congregation (The quest is called The Prince's Secret) Kurt and some guards will storm into the throne room and inform you that a Coup has started. If your relationship with Kurt is Friendly then he will take your side and help you stop it which will earn you
But will prevent this achievement from being obtainable.
If your relationship with Kurt is 'Suspicious' or 'Nice'then you will have to fight him in Constantin's throne room and kill him. This will unlock Betrayal in blood. I suggest saving as soon as you can as you will next have to pick between two cities to save from the Coup. You can only save one so choose the Alliance to obtain this achievement. Then load your save and choose to save the Thélème instead to obtain the following achievement: