We present the spectroscopic and photometric evolution of the nearby (z = 0.059) spectroscopically confirmed Type Ic supernova, SN 2010bh, associated with the soft, long-duration gamma-ray burst (X-ray flash) GRB 100316D. Intensive follow-up observations of SN 2010bh were performed at the ESO Very Large Telescope (VLT) using the X-shooter and FORS2 instruments. Thanks to the detailed temporal coverage and the extended wavelength range (3000-24800 Å), we obtained an unprecedentedly rich spectral sequence among the hypernovae, making SN 2010bh one of the best studied representatives of this SN class. We find that SN 2010bh has a more rapid rise to maximum brightness (8.0 ± 1.0 rest-frame days) and a fainter absolute peak luminosity (L bol ≈ 3 × 1042 erg s-1) than previously observed SN events associated with GRBs. Our estimate of the ejected 56Ni mass is 0.12 ± 0.02 M &sun;. From the broad spectral features, we measure expansion velocities up to 47,000 km s-1, higher than those of SNe 1998bw (GRB 980425) and 2006aj (GRB 060218). Helium absorption lines He I λ5876 and He I 1.083 μm, blueshifted by ~20,000-30,000 km s-1 and ~28,000-38,000 km s-1, respectively, may be present in the optical spectra. However, the lack of coverage of the He I 2.058 μm line prevents us from confirming such identifications. The nebular spectrum, taken at ~186 days after the explosion, shows a broad but faint [O I] emission at 6340 Å. The light curve shape and photospheric expansion velocities of SN 2010bh suggest that we witnessed a highly energetic explosion with a small ejected mass (E k ≈ 1052 erg and M ej ≈ 3 M &sun;). The observed properties of SN 2010bh further extend the heterogeneity of the class of GRB SNe.