Impact-stiffening materials that undergo a strain rate-induced soft-to-rigid transition hold great promise as soft armors in the protection of the human body and equipment. However, current impact-stiffening materials, such as polyborosiloxanes and shear-thickening fluids, often exhibit a limited impact-stiffening response. Herein, we propose a design strategy for fabricating highly impact-stiffening supramolecular polymer networks by leveraging high-entropy-penalty physical interactions. We synthesized a fully biobased supramolecular polymer comprising poly(α-thioctic acid) and arginine clusters, whose chain dynamics are governed by highly specific guanidinium-carboxylate salt-bridge hydrogen bonds. The resulting material exhibits an exceptional impact-stiffening response of ∼2100 times, transitioning from a soft dissipating state (21 kPa, 0.1 Hz) to a highly stiffened glassy state (45.3 MPa, 100 Hz) with increasing strain rates. Moreover, the material's high energy-dissipating and hot-melting properties bring excellent damping performance and easy hybridization with other scaffolds. This entropy-driven approach paves the way for the development of next-generation soft, sustainable, and impact-resistant materials.