Antonyms for the phrase "hast a shot at" could include terms like "give up," "resign oneself," or even "disregard." Each of these alternatives suggests a lack of enthusiasm, energy, or optimism, contrasting with the idea of pursuing or attempting to achieve something. To "give up" implies a complete surrender, often in the face of daunting obstacles or long odds. To "resign oneself" is a more passive, less dramatic alternative, indicating acceptance or acquiescence in the face of circumstances that cannot be changed. And to "disregard" suggests a level of indifference, in which an opportunity or challenge is seen as unworthy or irrelevant.