We study the Duffing equation \(\ddot{x}-x+x^3=0\) under time-periodic perturbations that preserve reversibility, i.e., the perturbed nonautonomous system remains invariant under the time reversal \(t\rightarrow -t\) and the involution \(R: (x,\dot{x})\rightarrow (-x,\dot{x})\) . This equation has a homoclinic figure-eight to the zero equilibrium, and we assume that the perturbed system becomes nonconservative. We show that, for small perturbations, the dynamics is dissipative in the sense that almost all orbits of the corresponding Poincaré map T from the interior of the figure-eight tend to a sink (respectively, a source) at forward (respectively, backward) iterations. It is a different matter when the amplitude of perturbation increases. Here, mixed dynamics as the phenomenon of intersection of an attractor with a repeller, becomes quite noticeable. Moreover, we propose two different bifurcation scenarios leading from simple dynamics to mixed dynamics. In the first scenario, mixed dynamics emerges as a result of the phenomenon known as the “attractor-repeller collision”. The second scenario leads to the instant appearance of chaos, when the previously observed simple regime (in our case, a stable fixed point) disappears and a chaotic regime – here, mixed dynamics – immediately comes to light.