Instruction tuning has emerged as a paramount method for tailoring the behaviors of LLMs. Recent work has unveiled the potential for LLMs to achieve high performance through fine-tuning with a limited quantity of high-quality instruction data. Building upon this approach, we further explore the impact of prompt's robustness on the selection of high-quality instruction data. This paper proposes a pioneering framework of high-quality online instruction data mining for instruction tuning, focusing on the impact of prompt's robustness on the data mining process. Our notable innovation, is to generate the adversarial instruction data by conducting the attack for the prompt of online instruction data. Then, we introduce an Adversarial Instruction-Following Difficulty metric to measure how much help the adversarial instruction data can provide to the generation of the corresponding response. Apart from it, we propose a novel Adversarial Instruction Output Embedding Consistency approach to select high-quality online instruction data. We conduct extensive experiments on two benchmark datasets to assess the performance. The experimental results serve to underscore the effectiveness of our proposed two methods. Moreover, the results underscore the critical practical significance of considering prompt's robustness.