We present the results of a set of high-resolution chemo-dynamical simulations of dwarf galaxies in a ΛCDM cosmology. Out of an original (3.4 Mpc/h)3 cosmological box, a sample of 27 systems are re-simulated from z = 70 to z = 0 using a zoom-in technique. Gas and stellar properties are confronted to the observations in the greatest details: in addition to the galaxy global properties, we investigated the model galaxy velocity dispersion profiles, half-light radii, star formation histories, stellar metallicity distributions, and [Mg/Fe] abundance ratios. The formation and sustainability of the metallicity gradients and kinematically distinct stellar populations are also tackled. We show how the properties of six Local Group dwarf galaxies, NGC 6622, Andromeda II, Sculptor, Sextans, Ursa Minor and Draco are reproduced, and how they pertain to three main galaxy build-up modes. Our results indicate that the interaction with a massive central galaxy could be needed for a handful of Local Group dwarf spheroidal galaxies only, the vast majority of the systems and their variety of star formation histories arising naturally from a ΛCDM framework. We find that models fitting well the local Group dwarf galaxies are embedded in dark haloes of mass between 5 × 108 to a few 109 M⊙, without any missing satellite problem. We confirm the failure of the abundance matching approach at the mass scale of dwarf galaxies. Some of the observed faint however gas-rich galaxies with residual star formation, such as Leo T and Leo P, remain challenging. They point out the need of a better understanding of the UV-background heating.Key words: galaxies: general / galaxies: dwarf / Galaxy: evolution / Galaxy: formation / galaxies: structure