The correct answer is A. To oppose with determination.
To set one’s face against something means to oppose it with determination. It can also mean to be opposed to something or to be against something.
Option B is incorrect because to judge by appearance means to judge someone or something based on how they look.
Option C is incorrect because to get out of difficulty means to find a way to solve a problem or to escape from a difficult situation.
Option D is incorrect because to look at one steadily means to look at someone without blinking or looking away.
Option E is incorrect because it is not a definition of the phrase “to set one’s face against.”