The present paper investigates the critical normal form coefficients for the one-parameter and two-parameter bifurcations of a discrete-time Bazykin–Berezovskaya prey-predator model. Based on the critical coefficients, it can be determined which scenario corresponds to each bifurcation. Further, for a better representation of the study, the complex dynamics of the model are investigated theoretically and numerically using MatcotM, which is a Matlab package. Some graphical representations of the model are presented to verify the obtained results. The outcome of the study reveals that the model undergoes multiple bifurcations including period-doubling, Neimark–Sacker, and strong resonance bifurcations.