From Longman Dictionary of Contemporary Englishbe on the horns of a dilemmabe on the horns of a dilemmaCHOOSEto be in a situation in which you have to choose between two equally unpleasant or difficult situations → horn
Examples from the Corpus
be on the horns of a dilemma• Stirling, who had come direct from Eighth Army Headquarters, was on the horns of a dilemma. 