Meet Damien at Count de la Croix's mill after midnight. Being at the mill at midnight will trigger a cutscene. Geralt and Damien plan their siege on the castle.
A cutscene will take you to the castle. Make your way through the castle guards. None of them are difficult to take down alone, but there are a lot of them. Use patience to find openings and mix up sign usage to eliminate them one by one. Taking out guards that wield crossbows first will help.
Keep making your way through the enemies until Dettlaff and Regis show up to save the day. Just stay out of their way as the mow down the remaining guards. After you, Dettlaff and Regis take out the resistance, the three will meet Syanna. That eventual conversation with the Duchess will complete the mission.