The phrase "hast a fling at" typically means to try something quickly or impulsively. Its antonyms would be to approach something with caution, thoughtfulness, and care. Some alternatives to hast a fling at include taking a deliberate approach, conducting a thorough investigation, and practicing due diligence. Other antonyms might include taking measured steps, approaching something systematically, or conducting a comprehensive analysis. Essentially, antonyms for "hast a fling at" are any methods that prioritize careful consideration and preparation over impulsiveness or rash decision-making.