The word "haddest fling at" is an idiom meaning to attempt or try something. There are several antonyms that can be used to replace this phrase depending on the context. If you want to express a lack of effort, you can use words like give up, surrender, or abandon. If you want to indicate failure or lack of success, you can use words like miss, fall short, or fail. Alternatively, if you want to indicate a successful attempt, you can use words like achieve, succeed, or conquer. The choice of antonym will depend on the tone and meaning that you want to convey.