Wave energy is one of the untapped renewable energy sources, requiring further development of wave energy converters (WECs) to become competitive with wind and solar energy. A significant challenge for WEC development is the high levelized cost of energy (LCoE) associated with traditional heaving or diffraction-based devices. However, analytical and experimental evaluation of lift-based cyclorotor WECs indicate that these devices can achieve superior power absorption when optimised using advanced control techniques, potentially increasing power production by several times, compared to uncontrolled scenarios. This work presents the first implementation of Nonlinear Model Predictive Control (NMPC) for a cyclorotor WEC. The control strategy relies on the separation principle, assuming accurate wave prediction over the control horizon for panchromatic waves. A comparison of various pitch and/or velocity control strategies is conducted for different irregular sea states. The results, obtained by simulations, confirm and exceed the capability, previously predicted by the theoretical optimal control solution, of a cyclorotor WEC to absorb up to 70% of wave energy.