The simultaneous presence of parameter variations, time-varying disturbances, and delay in the control loop of an $n{\text{th}}$-order (possibly unstable) dynamical system makes formal tracking control design difficult. Existing model-based control methodologies can handle only a subset of the above-mentioned complexities, and hence, become insufficient to accurately track the desired trajectory. In this paper, a prediction-based adaptive robust control framework is proposed for high performance control of dynamical systems subject to the above-mentioned complexities, which involves the following. First, prediction-based projection-type adaptation laws with model compensation to reduce the effect of parameter uncertainties under delay and time-varying disturbances. Second, a robust prediction scheme that factors in both unknown parameters and disturbance uncertainties under delay to handle the resulting unmatched disturbances. Third, prediction-based continuous robust feedback to attenuate the cumulative effect of disturbance terms due to uncertain prediction. The controller guarantees semiglobal, exponential convergence of the tracking error with an ultimate error bound proportional to delay, disturbance, and controller gain. The controller effectiveness is demonstrated with an illustrative flight control example and compared with the baseline adaptive robust controller.