Robust interfacial compliance is essential for long-term physiological monitoring via skin-mountable ionic materials. Unfortunately, existing epidermal ionic skins are not compliant and durable enough to accommodate the time-varying deformations of convoluted skin surface, due to an imbalance in viscosity and elasticity. Here we introduce a self-compliant ionic skin that consistently works at the critical gel point state with almost equal viscosity and elasticity over a super-wide frequency range. The material is designed by leveraging hierarchical hydrogen bond association, allowing for the continuous release of polymer strands to create topological entanglements as complementary crosslinks. By embodying properties of rapid stress relaxation, softness, ionic conductivity, self-healability, flaw-insensitivity, self-adhesion, and water-resistance, this ionic skin fosters excellent interfacial compliance with cyclically deforming substrates, and facilitates the acquisition of high-fidelity electrophysiological signals with alleviated motion artifacts. The presented strategy is generalizable and could expand the applicability of epidermal ionic skins to more complex service conditions.