When it comes to synonyms for the phrase "contest of strength," there are a few different options that can be used. For instance, you could use the term "battle of brawn" to describe a competition that's focused on physical strength. Alternatively, you might opt for "power struggle" as a way of conveying a more subtle competition that isn't strictly based on physical size or might. Other options include "test of might," "strongman showdown," and "tug of war." Ultimately, the best synonym for "contest of strength" will depend on the specific context in which it's being used, and the nuances of the competition at hand.