The phrase "with one's might" typically indicates using all of one's strength, power, and effort to accomplish a task or overcome an obstacle. Its antonyms would therefore connote less effort or force. Examples might include phrases such as "half-heartedly," "without conviction," or "lazily," in which an individual doesn't put forth much energy or enthusiasm. Other antonyms might refer to a more strategic or nuanced approach, such as "with finesse," or "with subtlety," where the focus is on achieving the goal without brute force. Ultimately, the opposite of "with one's might" would depend on the context in which it is being used and the specific desired outcome.