Silicon nitride (Si₃N₄) has emerged as a compelling platform for visible-light, quantum-photonic, and nonlinear-optical applications because of its broad transparency window, low propagation loss, and negligible two-photon absorption. However, the moderate refractive index of Si₃N₄ poses a challenge for efficient fiber-to-chip coupling using grating couplers. Although advantageous for wafer-scale testing and flexible layouts, Si₃N₄ grating couplers suffer from low grating strength, which limits their coupling efficiency. Here, we experimentally demonstrate high-efficiency grating couplers on a hybrid amorphous-silicon/silicon-nitride (a-Si/Si₃N₄) platform. Uniform devices are presented for TE and TM polarizations in both the O- and C-bands, while apodized-focalizing designs are demonstrated for both polarizations in the O-band and for TE polarization in the C-band. The fabricated devices achieved record coupling efficiencies of -1.6 dB and -1.2 dB in the O-band for TE and TM polarization, respectively, and -1.3 dB and -2.9 dB in the C-band for TE and TM polarization, respectively. The measured peak wavelengths deviated from their nominal values, primarily because of variations in the refractive index of the fabricated Si₃N₄ and the grating duty cycles relative to their design values. These shifts are well reproduced by simulations incorporating fabrication biases and can be compensated for by adjusting grating parameters or the fiber coupling angle. To the best of our knowledge, these are the highest coupling efficiencies demonstrated to date for silicon nitride grating couplers in the O-band for both polarizations and in the C-band for TM polarization. For TE polarization in the C-band, fabrication deviations shifted the peak coupling wavelength to 1512 nm, resulting in the highest efficiency reported to date for a silicon nitride grating coupler operating in the S-band. These results demonstrate a practical approach for achieving low-loss fiber-to-chip coupling in Si₃N₄ photonic integrated circuits, addressing a longstanding challenge in the platform and supporting the development of scalable systems for datacom, telecom, nonlinear photonics, and quantum technologies.