Hydrogels derived from 2-acrylamido-2-methyl-1-propanesulfonic acid (AMPS) monomer are attractive materials for producing soft-biomimetic actuators, superabsorbents, and biomaterials. Here we present a simple synthetic strategy to prepare mechanically strong poly(2-acrylamido-2-methyl-1-propanesulfonic acid) (PAMPS) hydrogels with self-healing ability. Initiator-free polymerization of AMPS in aqueous solution in the presence of Laponite nanoparticles and N,N'-methylenebis(acrylamide) (BAAm) cross-linker produces hybrid-cross-linked hydrogels with excellent mechanical properties. The hydrogels exhibit a high modulus (similar to 700 kPa), compressive strength (45 MPa at similar to 90% strain), good resilience, and self-healing. The results reveal that the incorporation of Laponite and BAAm separately into the physical PAMPS network weakens hydrogen bonding interactions while their combination enhances these interactions and generate water-insoluble hydrogels with a high modulus. The superior properties of hybrid cross-linked hydrogels are attributed to strengthening of the interactions between chemically cross-linked PAMPS chains and nanoparticles. The hybrid approach presented here might enable preparation of mechanically strong nanocomposite hydrogels consisting of strongly or weakly charged polymer chains of different architecture.