When certain negative adverbial phrases, such as "Under no circumstances," "Never," "Hardly ever," or "Not until," begin a sentence, they require inversion of the subject and auxiliary verb. This means the auxiliary verb comes before the subject, similar to a question structure.
Option B, "Under no circumstances should we enter the room," is the correctly structured sentence. Here, "should" is the auxiliary verb, and "we" is the subject. The inversion places "should" before "we," following the rule for negative adverbial fronting.
Options A, C, and D are incorrect because they do not apply the necessary inversion. In these options ("we should," "we must," "we will"), the subject "we" comes before the auxiliary or modal verb, which is grammatically incorrect after a negative adverbial phrase like "Under no circumstances." The correct structure emphasizes the strong prohibition.