We apply the minimum-energy paths (MEPs) approach to study the helix unwinding transition in chiral nematic liquid crystals. A mechanism of the transition is determined by a MEP passing through a first order saddle point on the free energy surface. The energy difference between the saddle point and the initial state gives the energy barrier of the transition. Two starting approximations for the paths are used to find the MEPs representing different transition scenarios: (a) the director slippage approximation with in-plane helical structures and (b) the anchoring breaking approximation that involves the structures with profound out-of-plane director deviations. It is shown that, at sufficiently low voltages, the unwinding transition is solely governed by the director slippage mechanism with the planar saddle-point structures. When the applied voltage exceeds its critical value below the threshold of the Freedericksz transition, the additional scenario through the anchoring breaking transitions is found to come into play. For these transitions, the saddle-point structure is characterized by out-of-plane deformations localized near the bounding surface. The energy barriers for different paths of transitions are computed as a function of the voltage and the anchoring energy strengths.