We aim at characterising the morphology and the physical parameters governing the shock physics of the Herbig-Haro object HH99B. We obtained SINFONI-SPIFFI IFU spectroscopy (R~2000-4000) between 1.10 and 2.45{mu}m detecting more than 170 emission lines, that, to a large extent, have never observed before in a Herbig-Haro object. Most of them come from ro-vibrational transitions of molecular hydrogen (v_up_<=7, E_up_~<38000K) and [FeII] (E_up_~<30000K). In addition, we observed several hydrogen and helium recombination lines, along with fine-structure lines of ionic species. All the brightest lines appear resolved in velocity. Intensity ratios of ionic lines were compared with predictions of NLTE models to derive bi-dimensional maps of extinction and electron density, along with estimates of temperature, fractional ionisation, and atomic hydrogen post-shock density. The H2 line intensities were interpreted in the framework of Boltzmann diagrams, from which we have derived extinction and temperature maps of the molecular gas. From the intensity maps of bright lines (i.e. H2 2.122{mu}m and [FeII]1.644{mu}m), the kinematical properties of the shock(s) at work in the region were delineated. Finally, from selected [FeII] lines, constraints on the spontaneous emission coefficients of the 1.257, 1.321, and 1.644{mu}m lines are provided.