We report a combined experimental characterization and theoretical modeling of the hexa-coordinated high-spin Co(ii) complex cis-[Co(hfac)2(H2O)2] (I). The magnetic static field (DC) data and EPR spectra (measurements were carried out on the powder samples of diluted samples cis-[Co0.02Zn0.98 (hfac)2(H2O)2]) were analyzed with the aid of the parametric Griffith Hamiltonian for the high-spin Co(ii) supported by the ab initio calculations of the crystal field (CF) parameters, g-factors and superexchange parameters between H-bonded Co(ii) ions in the neighboring molecules in a 1D network. This analysis suggests the presence of the easy axis of magnetic anisotropy and also shows the existence of a significant rhombic component. The detected frequency dependent (AC) susceptibility signal shows that complex I exhibits slow paramagnetic relaxation in the applied DC field belonging thus to the class of non-uniaxial field induced single ion magnets with a negative axial component of anisotropy. It is demonstrated that the main contributions to the relaxation come from the direct one-phonon process dominating at low temperatures, while the contribution of the two-phonon Raman process becomes important with increasing temperature.