High modulus, high strength hydrogels were prepared from crosslinked copolymers of N,N-dimethylacrylamide (DMA), 2-(N-ethylperfluoro-octane sulfonamido) ethyl methacrylate (FOSM) and cinnamoyloxyethylacrylate. These FOSM-Cinnamate hybrid hydrogels were composed of a physical network and a chemical network, both attached to the same polymer backbone, and the physical network was derived from a nanophase-separated microstructure of hydrophobic nanodomains. These hybrid hydrogels were viscoelastic with high shear modulus (30–400 kPa), which was mainly contributed by the physical crosslinks formed by the FOSM nanodomains. The covalent network provided a permanent shape for the hydrogel and the physical network provided a mechanism for high energy dissipation (tan δ reached values of 0.65 at high temperature). The dynamic properties were dependent on temperature, frequency and FOSM content. The hybrid hydrogels exhibited excellent tensile and compressive properties with tensile modulus of 51–184 kPa, ultimate tensile stress of 210–540 kPa, tensile elongation to break of 500–600%, fracture toughness of 52–188 J m−2; compressive modulus of 0.40–1.58 MPa, compressive strengths of 10.3–34.5 MPa and compressive strains of 80–85%. Compared to a physical hydrogel without covalent crosslinks, the hybrid hydrogels had much higher stiffness and strength, but lower extensibility. The hybrid hydrogels could be compressed over 80% without breaking and completely recovered their original shape when the stress was removed.