The bigshots used their big intelligent brains to come up with a perfect idea. They needed to do everything possible to weaken Anneshia as much as possible. Only then they would have the chance to hurt her badly with their powerful individuals.
The first method used against her was poison. At first they sacrificed a noble family to use a super deadly poison on her. But even that extremely deadly poison was not able to make her a little sick and nothing more. And that little sickness went away immediately after she used one Cocoon Break and she also gained poison resistance from this whole experiment.
She then interrogated the family and was even able to find a slight clue about a higher up who was actually responsible for this. She then did her own little investigation and that ended up with the destruction of a notable family.