Our recent study has revealed that neutral polyampholytes form tough physical hydrogels above a critical concentration Cm,c by forming ionic bonds of wide strength distribution. In this work, we systematically investigate the behavior of a polyampholyte system, poly(NaSS-co-DMAEA-Q), randomly copolymerized from oppositely charged monomers, sodium p-styrenesulfonate (NaSS) and acryloyloxethyltrimethylammonium chloride (DMAEA-Q) without and with a slight chemical cross-linking. A phase diagram of formulation has been constructed in the space of monomer concentration Cm and cross-linker density CMBAA. Three phases are observed for the as-synthesized samples: homogeneous solution at dilute Cm, phase separation at semi-dilute Cm, and homogenous gel at concentrated Cm. Above a critical Cm,c, the polyampholyte forms a supramolecular hydrogel with high toughness by dialysis of the mobile counter-ions, which substantially stabilizes both the intra- and inter chain ionic bonds. The presence of the chemical cross-linker (CMBAA > 0) brings about a shift of the tough gel phase to lower Cm,c. The tough polyampholyte gel, containing ∼50 wt% water, is highly stretchable and tough, exhibits fracture stress of σb∼ 0.4 MPa, fracture strain of εb∼ 30, and the work of extension at fracture Wext∼ 4 MJ m-3. These values are at the level of most tough soft materials. Owing to the reversible ion bonds, the poly(NaSS-co-DMAEA-Q) gels also exhibit complete self-recovery (100%) and high fatigue resistance upon repeated large deformation.