Antonyms for the phrase "hangs onto your hat" include expressions such as "stay calm", "relax", "take it easy", or "keep your composure". These phrases suggest that the situation is not as overwhelming or exciting as the original phrase implies, and that there is no need to hold on tight to anything. Other antonyms could be "let go", "release", or "give up", which suggest a sense of surrender or acceptance rather than defiance or determination. Depending on the context, a variety of opposites could be used to convey a sense of calm, restraint, or detachment, all of which contrast with the energy and urgency that "hang onto your hat" implies.