High-resolution microscopy hyperspectral (HS) images can provide highly detailed spatial and spectral information, enabling the identification and analysis of biological tissues at a microscale level. Recently, significant efforts have been devoted to enhancing the resolution of HS images by leveraging high spatial resolution multispectral (MS) images. However, the inherent hardware constraints lead to a significant distribution gap between HS and MS images, posing challenges for image super-resolution within biomedical domains. This discrepancy may arise from various factors, including variations in camera imaging principles (e.g., snapshot and push-broom imaging), shooting positions, and the presence of noise interference. To address these challenges, we introduced a unique unsupervised super-resolution framework named R2D2-GAN. This framework utilizes a generative adversarial network (GAN) to efficiently merge the two data modalities and improve the resolution of microscopy HS images. Traditionally, supervised approaches have relied on intuitive and sensitive loss functions, such as mean squared error (MSE). Our method, trained in a real-world unsupervised setting, benefits from exploiting consistent information across the two modalities. It employs a game-theoretic strategy and dynamic adversarial loss, rather than relying solely on fixed training strategies for reconstruction loss. Furthermore, we have augmented our proposed model with a central consistency regularization (CCR) module, aiming to further enhance the robustness of the R2D2-GAN. Our experimental results show that the proposed method is accurate and robust for super-resolution images. We specifically tested our proposed method on both a real and a synthetic dataset, obtaining promising results in comparison to other state-of-the-art methods. Our code and datasets are accessible through Multimedia Content.