We report measurements of magnetic quantum oscillations and specific heat at low temperatures across a field-induced antiferromagnetic quantum critical point (QCP)(B_{c0}approx50T) of the heavy-fermion metal CeRhIn_5. A sharp magnetic-field induced Fermi surface reconstruction is observed inside the antiferromagnetic phase. Our results demonstrate multiple classes of QCPs in the field-pressure phase diagram of this heavy-fermion metal, pointing to a universal description of QCPs. They also suggest that robust superconductivity is promoted by unconventional quantum criticality of a fluctuating Fermi surface.