We present the first results of a spectroscopic survey of faint lensed galaxies in the core of the galaxy cluster AC114 (z = 0.312) obtained from observations with the FORS1 spectrograph mounted on the VLT-Antu (Unit Telescope 1). The galaxies were chosen according to both lensing and photometric redshift criteria in areas close to the high-z critical lines predicted by the gravitational lens model of Natarajan et al. (NKSE, 1998) for this cluster. All the target galaxies are found to correspond to background galaxies with redshift values in the [0.7, 3.5] interval. Our spectroscopic observations confirm the predicted lensing redshifts for 3 of the multiply-imaged galaxies, and together with predictions of the NKSE model led to the discovery of a new 5-image configuration at redshift z = 3.347. A revised NKS model, compatible with the redshift of this new multiple-image system, was generated and employed to calculate the gravitational amplifications of all the observed galaxies. The galaxies corresponding to the multiple-image systems are found to be intrinsically fainter, between 0.5 and 1.5 magnitudes, than the limiting magnitudes of existing blank field studies. When all the observed background galaxies are considered, the resulting intrinsic absolute magnitudes range from M-B similar to -22 to -19, with a median value of -20.5. Therefore, a large gain in sensitivity towards low luminosity high-z objects can actually be obtained, in agreement with theoretical expectations. This method can be used advantageously to probe the high redshift Universe and, in particular, its application to an ensemble of massive cluster cores could constraint the faint end of luminosity function of high redshift galaxies.