A fully microscopic molecular hydrodynamic theory for the third-order Raman spectrum of an atomic liquid (Xe) is presented. The spectrum is obtained from a mode-coupling theory by projecting the dynamics onto bilinear pairs of fluctuating density variables. For the densities and temperatures studied, semiquantitative agreement is obtained in comparison with molecular dynamics simulation on all time scales. The theory is contrasted with previous molecular hydrodynamic theories of depolarized light scattering spectra. Extensions of the approach outlined here to both classical molecular and quantum liquids are presented. The theory presented here represents the first microscopic solvation theory which quantitatively captures both the inertial and long-time dynamics as well as the crossover between these regimes.