This paper studies the non-autonomous non-Newtonian micropolar fluids in
two-dimensional bounded domains. We first establish that the generated
continuous process of the solutions operator possesses a pullback
attractor. Then we verify the existence of statistical solutions by
constructing the invariant Borel probability measures. Further, we prove
that the statistical solutions possess the degenerated regularity of
Lusin's type provided that the Grasshof number associated to the
external forces is small enough.