In the immediate vicinity of the critical temperature (T_{c}) of a phase transition, there are fluctuations of the order parameter that reside beyond the mean-field approximation. Such critical fluctuations usually occur in a very narrow temperature window in contrast to Gaussian fluctuations. Here, we report on a study of specific heat in graphite subject to a high magnetic field when all carriers are confined in the lowest Landau levels. The observation of a BCS-like specific heat jump in both temperature and field sweeps establishes that the phase transition discovered decades ago in graphite is of the second order. The jump is preceded by a steady field-induced enhancement of the electronic specific heat. A modest (20%) reduction in the amplitude of the magnetic field (from 33 to 27 T) leads to a threefold decrease of T_{c} and a drastic widening of the specific heat anomaly, which acquires a tail spreading to two times T_{c}. We argue that the steady departure from the mean-field BCS behavior is the consequence of an exceptionally large Ginzburg number in this dilute metal, which grows steadily as the field lowers. Our fit of the critical fluctuations indicates that they belong to the 3DXY universality class as in the case of the ^{4}He superfluid transition.