The study investigates the impact of the density ratio [Formula presente] on droplet breakup for non-Newtonian fluids using numerical simulations. An in-house solver based on OpenFOAM version 4.x libraries and coupled Level Set - Volume of Fluid method for interface capturing is employed. Non-Newtonian rheology was modelled as power-law fluid with power-law index varying from 0.2-1.8 to simulate both shear thinning and shear thickening fluid regimes. A parametric study consisting of 65 two-dimensional axisymmetric simulations were performed to analyse the secondary breakup after different ?r. Correction factors have been proposed to the estimation of critical Weber number (Wecr) for first and second critical droplet breakup for power law fluids. The resulting Wecr formulation was found be within +/- 2 of the present simulation dataset. The study further examines the near vicinity flow field and discusses the flow dynamics like Hill and Wake vortices, their growth and vortex strength due to the combined effect of density ratio and non-Newtonian rheology. The effect of density ratio on deformation ratio and deformation rate at flow balancing and initiation points were incorporated in the Internal Flow Theory (IFT) for power law fluids. Lastly, effect of the density ratio and power-law index on Werim has been analysed.