We consider the problem of designing a low-complexity, approximation-free, output-feedback controller to achieve output tracking with prescribed transient and steady-state performance for uncertain, high relative degree, multi-input-multi-output (MIMO) nonlinear systems, which are equivalent via a diffeomorphic coordinate transformation to the Byrnes-Isidori canonical form, with uniform-bounded-input-bounded-state (UBIBS) stable internal dynamics and bounded external disturbances. The proposed controller utilizes the prescribed performance control methodology and high-gain observers. To avoid the propagation of the peaking phenomenon, the developed controller is appropriately saturated without compromising the closed-loop system performance attributes. Moreover, the selection of the observer gains is significantly relaxed owing to the fact that the adopted prescribed performance control technique seeks only for boundedness properties to establish the desired transient and steady-state performance specifications. Finally, various simulation studies clarify and verify the approach.