This study presents an optimization model for battery scheduling in Advanced Air Mobility (AAM) operations considering congested (peak-hour) flight periods. Peak-hour demand concentration causes bottlenecks in vertiport charging/swapping facilities and accelerates battery degradation, reducing operational efficiency. A Mixed-Integer Linear Programming (MILP) model is developed, incorporating battery states (SoC, SoH), charger and swap-bay constraints, and power peak limits. Simulation results under peak and off-peak scenarios show that the proposed model reduces both delay time and total operating cost compared to average-demand scheduling. This study provides a quantitative decision-making basis for enhancing resource efficiency in AAM operations. The findings offer practical implications for improving AAM infrastructure efficiency and resource management policies.