The Generative Adversarial Network (GAN) is a powerful and flexible tool that can generate high-fidelity synthesized data by learning. It has seen many applications in simulating events in High Energy Physics (HEP), including simulating detector responses and physics events. However, training GANs is notoriously hard and optimizing their hyperparameters even more so. It normally requires many trial-and-error training attempts to force a stable training and reach a reasonable fidelity. Significant tuning work has to be done to achieve the accuracy required by physics analyses. This work uses the physics-agnostic and high-performance-computer-friendly hyperparameter optimization tool HYPPO to optimize and examine the sensitivities of the hyperparameters of a GAN for two independent HEP datasets. This work provides the first insights into efficiently tuning GANs for Large Hadron Collider data. We show that given proper hyperparameter tuning, we can find GANs that provide high-quality approximations of the desired quantities. We also provide guidelines for how to go about GAN architecture tuning using the analysis tools in HYPPO.