This paper investigates the prescribed performance attitude tracking problem for the rigid spacecraft subject to external disturbances and multiple constraints, including input saturation and full-state constraints. By employing the barrier Lyapunov function and an error-shifting transformation, a fixed-time tracking control strategy is devised capable of dealing with the prescribed performance problem under a completely unknown initial tracking condition. In addition, an auxiliary system is also introduced to compensate the adverse effect arising from the input saturation. Finally, the performance of the proposed control schemes is demonstrated by numerical simulations.