We report a magnetic field dependence of fluorescence of diamond single crystals containing NV$^-$ centers. In such spectra, numerous sharp lines are found, which correspond to Level Anti-Crossings (LACs) in coupled spins systems comprising an NV$^-$ center. Theoretical modeling of such LAC-spectra enables characterization of paramagnetic defect centers and determination of their magnetic resonance parameters, such as zero-field splitting and hyperfine coupling constants. The outlined method thus enables sensitive detection of paramagnetic impurities in diamond crystals.