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Orthorhombic molybdenum trioxide (alpha-MoO3), a newly discovered polaritonic van der Waals crystal, is attracting significant attention due to its strongly anisotropic mid-infrared phonon-polaritons. At the same time, coupling of polariton with its mirror image in an adjacent metal gives rise to a significantly more confined image mode. Here, monocrystalline gold flakes-an atomically flat low-loss substrate for mid-infrared image polaritons-are employed to measure the full complex-valued propagation constant of the hyperbolic image phonon-polaritons in alpha-MoO3 by near-field probing. The anisotropic dispersion is mapped and the damping of the polaritons propagating at different angles to the crystallographic directions of alpha-MoO3 is analyzed. These experiments demonstrate the strongly confined image phonon-polaritons in alpha-MoO3 exhibiting intrinsic limiting lifetime of 4.2 ps and a propagation length of 4.5 times the polariton wavelength, owing to the negligible substrate-mediated loss. Furthermore, it is shown that the image modes with positive group velocity have simultaneously larger momentum and lifetime compared to their counterparts on a dielectric substrate, while the image modes with negative group velocity possess a smaller momentum. These results spotlight the hyperbolic image phonon-polaritons as a superior platform for unconventional light manipulation at the nanoscale.