To develop trustworthy Vision-Language Models (VLMs), it is essential to address adversarial robustness and hallucination mitigation, both of which impact factual accuracy in high-stakes applications such as defense and healthcare. Existing methods primarily focus on either adversarial defense or hallucination post-hoc correction, leaving a gap in unified robustness strategies. We introduce \textbf{Hydra}, an adaptive agentic framework that enhances plug-in VLMs through iterative reasoning, structured critiques, and cross-model verification, improving both resilience to adversarial perturbations and intrinsic model errors. Hydra employs an Action-Critique Loop, where it retrieves and critiques visual information, leveraging Chain-of-Thought (CoT) and In-Context Learning (ICL) techniques to refine outputs dynamically. Unlike static post-hoc correction methods, Hydra adapts to both adversarial manipulations and intrinsic model errors, making it robust to malicious perturbations and hallucination-related inaccuracies. We evaluate Hydra on four VLMs, three hallucination benchmarks, two adversarial attack strategies, and two adversarial defense methods, assessing performance on both clean and adversarial inputs. Results show that Hydra surpasses plug-in VLMs and state-of-the-art (SOTA) dehallucination methods, even without explicit adversarial defenses, demonstrating enhanced robustness and factual consistency. By bridging adversarial resistance and hallucination mitigation, Hydra provides a scalable, training-free solution for improving the reliability of VLMs in real-world applications.