Eini didn't have the slightest idea that her sister had already threatened the principal, so her first idea was to make Shiba's value for the academy increase to a level that even if the conflict between him and Bea were unveiled, the academy wouldn't side with Bea.
Bea was quite hated by the students of the academy. Even those who tried to win her favor didn't really like her, so as long as the academy didn't decide to side with her, it would be easy to gain the support of the other students if the conflict was to make public.
It was similar to how Reia had a lot of support of the students in her attempts to surpass Bea in the competition since she was talented enough for the academy to not interfere with the conflict.
If she managed to beat Bea, acting against her later would be easier since Eini felt confident that Reia would be on their side against Bea even if they wanted to kill her.
