We investigate the trajectory tracking problem of a quadrotor-slung-load system with unknown load mass in the presence of pre-specified performance specifications imposed on both the position of the load and the cable direction. In contrast to existing literature where performance bounds are only function of time, here we propose a revised performance bound which is also function of the tracking errors associated with the slung load subsystem. The unknown load mass is obtained from an adaptive law that is designed within the framework of backstepping. All system errors are shown to be uniformly ultimately bounded, with simultaneous guarantees of prescribed accuracy and constraint satisfaction. Finally, simulation results are presented to validate and assess the effectiveness and robustness of the proposed methodology.