One possible synonym for the phrase "was on one tail" is "was relentless." This describes a person or group that is determined and unwavering in their pursuit of a goal or objective. Another synonym could be "dogged," which describes a persistent effort in the face of challenges or obstacles. "Tenacious" is another synonym that conveys a similar meaning, indicating a strong will and determination to achieve a desired outcome. Overall, these synonyms suggest a sense of focus, intensity, and determination, emphasizing the importance of persistence in achieving success.