The phrase "look square in the eye" is often used to convey a sense of determination or confrontation. There are several synonyms that can be used to express this same idea. One option is to use the phrase "stare down," which emphasizes the idea of making direct eye contact and standing firm in the face of opposition. Another option is to use the expression "face head-on," which conveys a similar sense of determination while also emphasizing the need to confront a situation directly. Other potential synonyms include "confront," "challenge," "meet head-on," and "stand up to," all of which imply a willingness to face difficult situations with strength and courage.