Antonyms for the phrase "has a fling at" could include "avoids," "ignores," or "abdicates responsibility." These phrases imply a lack of action or engagement with the task at hand, rather than actively pursuing it. Alternately, one could say that someone "diligently" or "meticulously" approaches the same task, indicating a careful and thoughtful approach rather than a fleeting attempt. Additionally, phrases like "commits to," "dedicates oneself to," or "deliberately undertakes" could indicate a deeper level of involvement and investment in the task, rather than just dipping one's toe in the water. Overall, finding an antonym for a phrase like "has a fling at" is about finding a phrase that conveys more commitment and determination.