The exploration of under-ice environments presents unique challenges due to limited access for scientific research. This report investigates the potential of deploying a fully actuated Remotely Operated Vehicle (ROV) for shallow area exploration beneath ice sheets. Leveraging advancements in marine robotics technology, ROVs offer a promising solution for extending human presence into remote underwater locations. To enable successful under-ice exploration, the ROV must follow precise trajectories for effective localization signal reception. This study develops a multi-input-multi-output (MIMO) nonlinear system controller, incorporating a Lyapunov-based stability guarantee and an adaptation law to mitigate unknown environmental disturbances. Fuzzy logic is employed to dynamically adjust adaptation rates, enhancing performance in highly nonlinear ROV dynamic systems. Additionally, a Particle Swarm Optimization (PSO) algorithm automates the tuning of controller parameters for optimal trajectory tracking. The report details the ROV dynamic model, the proposed control framework, and the PSO-based tuning process. Simulation-based experiments validate the efficacy of the methodology, with experimental results demonstrating superior trajectory tracking performance compared to baseline controllers. This work contributes to the advancement of under-ice exploration capabilities and sets the stage for future research in marine robotics and autonomous underwater systems.