Conductive hydrogels possess a remarkable potential for applications in soft electronics and robotics, owing to their unique combination of high electrical conductivity, stretchability, and impressive self-healing capabilities. However, the limited strength and toughness of these hydrogels have traditionally impeded their practical implementation. Inspired by the hierarchical architecture of high-performance biological composites found in Nature, in this study we successfully fabricate a novel type of strong and tough conductive hydrogel through self-assembly-induced bridge crosslinking of MgB2 nanosheets and polyvinyl alcohol (PVA) hydrogels. By combining the micro- to nano-level hierarchical lamellar structures of the PVA hydrogels with the robust molecular-level B-O covalent bonds, the resulting conductive hydrogel exhibits an exceptional strength of 8.58 to 32.7 MPa and a high toughness of 27.56 to 123.3 MJ/m3. Moreover, the hydrogel demonstrates exceptional sensitivity (with a response/relaxation time of 20 ms and a detection lower limit of ~1Pa) under external deformation, due to its nanoscale MgB2 nanosheets/PVA lamellar structure and extremely low compressive modulus. These unique characteristics enable the conductive hydrogel to exhibit superior performance in advanced soft sensing applications, particularly in non-contact speaking detection. This study represents a major breakthrough, introducing a new class of conductive hydrogel that integrates exceptional strength, toughness, and sensitivity, thereby opening up exciting possibilities for the development of high-performance conductive hydrogels.