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On a bounded smooth domain $\mathrm{\Omega }\subset {ℝ}^3$, we consider the generalized oscillon equation $${\partial }_{tt}u(x,t)+\omega (t){\partial }_{t}u(x,t)-\mu (t)\mathrm{\Delta }u(x,t)+V^{\prime }(u(x,t))=0,x\in \mathrm{\Omega }\subset {ℝ}^3,t\in ℝ$$ with Dirichlet boundary conditions, where $\omega$ is a time-dependent damping, $\mu$ is a time-dependent squared speed of propagation, and $V$ is a nonlinear potential of critical growth. Under structural assumptions on $\omega$ and $\mu$ we establish the existence of a pullback global attractor $𝒜=𝒜(t)$ in the sense of [1]. Under additional assumptions on $\mu$, which include the relevant physical cases, we obtain optimal regularity of the pull-back global...