Disc-shaped Autonomous Underwater Helicopters (AUHs) offer superior maneuverability but suffer from high hydrodynamic drag, which limits their operational endurance. To address this challenge, this study proposes a robust optimization framework for a novel sea-turtle-inspired AUH. A parametric hull, governed by two dimensionless shape factors based on modified Myring equations, was established to facilitate systematic exploration. To reduce the high computational cost of direct CFD evaluations, a high-precision Gaussian Process Regression (GPR) surrogate model was constructed from a small dataset of 24 samples. The core methodological innovation is T-NSGA-II, an algorithm featuring hyperparameters that are systematically optimized by the Optuna framework. In comparative evaluations, the T-NSGA-II-generated Pareto front demonstrated clear superiority over the standard NSGA-II, identifying designs with significantly lower drag for an equivalent vertical force. A key scientific contribution of this research is the identification of a distinct performance gap on the Pareto front. This phenomenon is interpreted not as an algorithmic artifact but as a ‘natural gap’, reflecting a deep physical trade-off, with potential underlying causes including a critical transition in flow physics or a topological shift in the optimal hull geometries. This work not only delivers a suite of optimized, practical AUH designs but also presents a powerful, intelligent optimization methodology that is capable of revealing fundamental physical trade-offs in complex engineering problems.