Catastrophic phase inversion, the breakdown of a concentrated emulsion characterized by the most puzzling sudden feature, is crucial in numerous industrial applications. Here we combine well-controlled experiments and fully resolved numerical simulations to study the critical dynamics of catastrophic phase inversion in oil-water emulsions under turbulent flow as the phase-inversion volume fraction is approached. We reveal that the phase inversion is characterized by the critical power-law divergence of fluctuations in the global drag force. We determine the enhanced dynamical heterogeneity in the local droplet structures at approaching the phase inversion, and tightly connect it to the diverging drag fluctuations. Moreover, we show that near to the critical point the phase inversion is triggered as a stochastic process by large fluctuations at both large and small scales. Our findings pave the way to modeling the phase inversion process as an out-of-equilibrium critical-like phenomena.