In this work, a robust controller design methodology for a broad class of singularly perturbed nonlinear systems with time-varying uncertainties is developed. When the fast subsystem is stabilizable and the slow subsystem is input/output linearizable with input-to-state stable (ISS) inverse dynamics, the developed state feedback controller guarantees boundedness of the trajectories of the closed-loop system and robust output tracking with arbitrary degree of asymptotic attenuation of the effect of uncertainty on the output, for initial conditions and uncertainties in an arbitrarily large compact set, so long as the singular perturbation parameter is sufficiently small. The controller is a continuous function of the state of the system and its construction requires the knowledge of bounding functions on the size of uncertainty. The developed method is applied to a non-isothermal continuous stirred tank reactor with fast jacket dynamics.