This paper investigates a predefined-time compound tracking control scheme for hybrid-actuator missiles to address the concurrent challenges posed by external disturbances, actuator saturation, and partial actuator failures. An improved predefined-time prescribed performance function (PTPPF) with single-sided monotonic boundaries is proposed to confine tracking errors within preassigned ranges, which effectively suppresses potential overshoot and prevents excessive initial control commands. By combining the improved PTPPF with a novel nonsingular sliding mode manifold based on hyperbolic functions, a predefined-time prescribed performance control (PTPPC) is developed to guarantee accelerated convergence and superior transient tracking performance. Besides, an auxiliary system is introduced to compensate for mismatches between virtual and actual control inputs caused by actuator saturation and allocation inaccuracies, which can effectively enhance overall control accuracy. Furthermore, a predefined-time adaptive control allocation (PTACA) strategy is designed to dynamically distribute virtual control commands among aerodynamic surfaces and lateral thrusters. The proposed PTACA explicitly accounts for actuator saturation and partial actuator failures, which improves control efficiency and minimises energy utilisation. The theoretical stability of the entire control framework is established via Lyapunov analysis. Finally, comparative numerical simulations are conducted to validate the effectiveness and superiority of the proposed scheme.