The phrase "horns of a dilemma" refers to a difficult choice between two equally unfavorable options. Some synonyms that can be used in place of this phrase include "rock and a hard place," "between a devil and the deep blue sea," "damned if you do, damned if you don't," and "two-edged sword." All of these phrases express the idea of being stuck in a difficult situation with no easy way out. While these phrases may not be interchangeable in all situations, they can still be useful alternatives to help convey the sense of feeling trapped or uncertain when faced with a challenging decision.