The phrase 'within a hair of' means something is extremely close or nearly happened. Synonyms for this phrase could be almost, on the cusp, inches away, narrowly missed, nearly achieved or just about. Other alternatives could be under the wire, on the verge, close to, bordering on, just shy, or within shooting distance. Additionally, within a whisker, close call, touching distance, close to the edge, on the brink, at the threshold, almost there, and just short of could also be used as synonyms for 'within a hair of'. These phrases help to better emphasize how close something or someone was to the desired result or goal.