There are several synonyms for the phrase "show a bold front", such as "project confidence", "display courage", "exhibit bravery", "demonstrate fearlessness", "manifest audacity", and "express boldness". The phrase can be used to describe someone displaying a strong and confident attitude in the face of adversity or difficult circumstances. It can be applied to various situations, such as a speaker addressing a hostile audience or a soldier standing firm in battle. These synonyms convey the idea of putting on a brave face and not showing any signs of weakness or fear, even when faced with a daunting challenge.