We perform the nuclear dynamics simulation to calculate the broad band as well as better resolved (a) photodetachment spectra of nitrogen dioxide anion (NO$^-_2$), and (b) photoelectron spectra of benzene radical cation (C₆H$^+_6$) with degeneracy among the electronic states using our parallelized time dependent discrete variable representation approach. For this purpose, we first consider a theoretical model that describes the photodetachment spectrum originating due to the Franck-Condon (FC) transition from the anionic ground state to the conically intersecting $\widetilde{X}^2 A_1 - \widetilde{A}^2 B_2$ electronic manifold of the neutral NO₂, whereas two multi-state, multi-mode model Hamiltonians of C₆H$^+_6$ with degeneracy among the electronic states are explored for its’ photoelectron spectra. The dynamics of C₆H$^+_6$ has been carried out with two Hamiltonians: (a) one consists with four states and nine modes, and (b) the other is constituted with three states and seven modes. Since the electronic states of both the systems are interconnected by several conical intersections in the vicinity of the FC region, it would be challenging to persue the dynamical calculation due to the impact of non-adiabaticity among the electronic states. The spectral profiles obtained with the advent of TDDVR approach show reasonably good agreement with the results obtained by other theoretical methodologies and experimental measurements.