<p>This paper completes classification on dynamics of a generalized Leslie–Gower model with the Holling type II functional response, posed in 2003, in the slow–fast setting by utilizing both the theories of singular perturbation (SP) and nonstandard SP together with some new technical treatments. The previous results on this model are only boundedness of the solutions, global stability of the equilibrium, existence of a stable limit cycle, and existence of a relaxation oscillation under some specified conditions. Here by our complete classification on the global dynamics, we not only prove existence of two limit cycles but also provide deformation of the cycles. Moreover, we also find several new dynamic phenomena, such as the beard cycle explosion, canard cycle explosion via transitory beard to relaxation oscillation, which were never found in any previous study among other models. Moreover, the application of the quantity <i>A</i>, in determining the singular Hopf bifurcation at a canard point, has been extended and developed.</p>