<p>Robust flight control design requires satisfying stability and performance requirements across a continuous flight envelope. Embedding this verification within a gain tuning loop creates a bi-level optimization: an outer optimizer searches for controller parameters while an inner worst-case search identifies the most critical envelope condition. Each evaluation in the inner loop demands nonlinear simulation, trimming, and linearization, driving the total computational cost to prohibitive levels. A surrogate-assisted framework is proposed in which Kriging models trained on the joint space of controller gains and envelope parameters replace direct simulation in the inner loop. Multiple worst-case candidates are determined by the surrogate using an Upper Confidence Bound criterion at varying confidence levels, guarding against surrogate inaccuracy. Only these candidates are passed to the true model, limiting costly evaluations to a small fixed number per outer iteration. Simulation failures at envelope boundaries are handled robustly without disrupting the optimization. The approach is demonstrated on the robust gain tuning of a large co-axial multicopter, achieving envelope-wide requirement satisfaction at a fraction of the direct simulation cost.</p>