This paper investigates the prescribed performance attitude tracking control problem of a rigid spacecraft with uncertain dynamics and bounded disturbances. By suitable selection of the configuration error function, the trajectory tracking problem on SO(3) is transformed into a point stabilisation problem of an error dynamic system in the associated Lie algebra. The predefined transient performance indexes, which include the maximum steady-state error and overshoot, and the minimum convergence rate of the attitude error vector, are characterised as the inequality constraints. For the tracking controller design, the error transformation technique is utilised to transform the attitude error dynamics with inequality constraints to an equivalent 'unconstrained' error one. Then, a coordinate-free robust tracking controller is designed for the 'unconstrained' error dynamics to solve the prescribed performance attitude tracking control problem. A rigorous mathematical stability proof is given. Finally, numerical simulations are presented to demonstrate the effectiveness and robustness of the proposed controller.