At the interface between two fluid layers in relative motion, minimal fluctuations are exponentially amplified, inducing vorticity and laminar flow breakdown. This process, known as Kelvin-Helmholtz instability, is responsible for many well-known phenomena observed in the atmosphere, ocean, and astrophysics, and is one of the exemplary pathways to turbulence in fluid dynamics. is. In classical fluid dynamics, instabilities are governed by universal scaling laws, but the extent to which universality manifests itself in quantum fluids is not yet fully understood. Here we shed light on this question by inducing Kelvin-Helmholtz instabilities of atomic superfluids over widely different regimes, from weakly interacting bosons to strongly correlated fermions versus condensates. We design two counter-rotating flows with adjustable relative velocities and observe how their contact interface evolves into a regular circular array of quantized vortices. It loses stability and winds up in clusters, closely resembling the classical Kelvin-Helmholtz dynamics. We extract the instability growth rates by tracking the positions of individual eddies and find that they follow a universal scaling relationship predicted by both classical hydrodynamics and microscopic point eddy models. bottom. Our results link quantum and classical fluids, reveal how the motion of quantized vortices reflects interfacial dynamics, and explain the spontaneous behavior of two-dimensional quantum turbulence from phase transitions in vortex-matter. It paves the way for exploring a wealth of non-equilibrium phenomena until emergence.