In this paper we report on the two-year-long Fermi-LAT observation of the peculiar blazar 4C +21.35 (PKS 1222+216). This source was in a quiescent state from the start of science operations of the Fermi Gamma-ray Space Telescope in 2008 August until 2009 September, and then became more active, with gradually increasing flux and some moderately-bright flares. In 2010 April and June, 4C +21.35 underwent a very strong GeV outburst composed of several major flares characterized by rise and decay timescales of the order of a day. During the outburst, the GeV spectra of 4C +21.35 displayed a broken power-law form with spectral breaks observed near 1-3 GeV photon energies. We demonstrate that, at least during the major flares, the jet in 4C +21.35 carried a total kinetic luminosity comparable to the total accretion power available to feed the outflow. We also discuss the origin of the break observed in the flaring spectra of 4C +21.35. We show that, in principle, a model involving annihilation of the GeV photons on the He II Lyman recombination continuum and line emission of broad line region clouds may account for such. However, we also discuss the additional constraint provided by the detection of 4C +21.35 at 0.07-0.4 TeV energies by the MAGIC telescope, which coincided with one of the GeV flares of the source. We argue that there are reasons to believe that the $lesssim$,TeV emission of 4C +21.35 (as well as the GeV emission of the source, if co-spatial), is not likely to be produced inside the broad line region zone of highest ionization ($sim 10^{17}$,cm from the nucleus), but instead originates further away from the active center, namely around the characteristic scale of the hot dusty torus surrounding the 4C +21.35 nucleus ($sim 10^{19}$,cm).
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