Energetic electrons have been frequently observed during magnetic reconnection in the magnetotail. The acceleration process of the energetic electrons is not fully understood. In this paper, we select for a detailed study a case of energetic electron acceleration from the earlier reported interval of turbulent magnetic reconnection in Earth's magnetotail observed by the Magnetospheric Multiscale mission. We use the first-order Taylor expansion method to reconstruct the magnetic topology of electron acceleration sites from the data. We find that the energetic electron fluxes increase inside the flux rope forming in front of the magnetic pileup region. We show that the energetic electrons are produced by a two-step process where two different acceleration mechanisms are successively operating outside and inside the flux rope. First, the thermal electrons are energized in the field-aligned direction inside the magnetic pileup region owing to the Fermi mechanism forming a cigar-like distribution. Second, those energized electrons are further accelerated predominately antiparallel to the magnetic field direction by a parallel electric field inside the flux rope. Our findings provide information for a better understanding of the generation of energetic electrons during turbulent reconnection process.