The phrase "hath a fling at" refers to making a sudden or risky attempt at something. Antonyms for this phrase would include words or phrases that imply caution, hesitation, or thoughtful action. Some antonyms might include "proceeding carefully," "taking a measured approach," "exercising caution," or "moving deliberately." Other antonyms might suggest a lack of action or decision-making altogether, such as "waiting to proceed," "avoiding risk," or "holding back." When choosing antonyms for "hath a fling at," it is important to consider the context in which the phrase is being used and what type of tone or message the writer or speaker is trying to convey.