Advancements in dialogue systems powered by large language models (LLMs) have outpaced the development of reliable evaluation metrics, particularly for diverse and creative responses. We present a benchmark for evaluating the robustness of reference-free dialogue metrics against four categories of adversarial attacks: speaker tag prefixes, static responses, ungrammatical responses, and repeated conversational context. We analyze metrics such as DialogRPT, UniEval, and PromptEval -- a prompt-based method leveraging LLMs -- across grounded and ungrounded datasets. By examining both their correlation with human judgment and susceptibility to adversarial attacks, we find that these two axes are not always aligned; metrics that appear to be equivalent when judged by traditional benchmarks may, in fact, vary in their scores of adversarial responses. These findings motivate the development of nuanced evaluation frameworks to address real-world dialogue challenges.