The viscoelastic and mechanical behaviors of physically cross-linked copolymer hydrogels synthesized from N,N-dimethylacrylamide (DMA) and 2-(N-ethylperfluorooctane sulfonamido)ethyl acrylate (FOSA) with varying FOSA concentration were studied by rheological and static tensile tests. The strong hydrophobic association of the FOSA moieties in an aqueous environment produced core–shell nanodomains that provided the physical cross-links. These PDMA–FOSA hydrogels exhibited excellent mechanical properties, including a modulus of ∼130–190 kPa, elongation at break of 1000–1600%, and ∼500 kPa tensile strength, depending on the FOSA concentration. The physical gels were more viscous than comparable chemical gels and were much more efficient at dissipating stress. The latter characteristic produced relatively high tensile toughness, ∼4–6 MPa, because of the extra energy dissipation mechanism provided by the reversible, hydrophobic cross-links. The PDMA–FOSA hydrogel exhibited peculiar dynamic behavior which was greatly dependent on temperature. At 25 °C, the hydrogel was highly elastic, but as the temperature increased, its viscous behavior increased and a crossover of the dynamic moduli (i.e., G″ > G′) occurred at 55 °C, as the rheological characteristics of the material went from a viscoelastic solid to a viscoelastic liquid. That behavior is a consequence of the physical nature of the structure of the physical cross-links and the dynamic nature of hydrophobic associations, which are influenced by composition, temperature, and time.