Robust domain adaptation against adversarial attacks is a critical area of research, addressing the need for models to perform consistently across diverse, challenging domains. In this paper, we derive a new generalization bound for robust risk on a target domain, using a novel divergence measure specifically tailored for robust domain adaptation. Inspired by this generalization bound, we propose a new algorithm named TAROT, which is designed to enhance domain adaptability and robustness. Additionally, we empirically demonstrate that a simple pseudo labeling approach, when combined with robust pretraining (Robust-PT), establishes a surprisingly strong baseline that surpasses traditional robust domain adaptation algorithms. Through extensive experiments, we illustrate that TAROT not only outperforms state-of-the-art methods in accuracy and robustness but also shows substantial scalability improvements. This improvements are done particularly in the challenging DomainNet benchmark dataset, emphasizing our algorithm's effectiveness and potential for broader applications.