A Dangerous Secret is an achievement for discovering who was behind the "accident" during the horse ride. It is pre-requisite for the achievement "Miracle Worker" during the week 4 trial.
During the invitation phase of the morning, you receive one of three versions of the same note with unfamiliar writing (see Letters). Choose to share the letter with Jasper and ask for his help.
On Waterday night you optionally have an event with Avalie, where, if you have > 170 interpersonal insight, you can learn more about the threat. This event is not required for the achievement.
Any day prior to Windday
Visit the forbidden wing and pass a check agains > 125 quick wits to gain information and +5 Secrets.
If you gained the necessary secret you will have an option to say that you suspect who your hidden enemy might be. This is not required, but good to check that you're on track.
If you did everything right, then after the matchmaker's interview Jasper will speak to you in your room and warn you not to do anything rash.