A four-pixel-array superconducting transition-edge sensor (TES) microcalorimeter with a mushroom-shaped absorber was fabricated for the energy dispersive spectroscopy performed on a transmission electron microscope. The TES consists of a bilayer of Au/Ti with either a 50-nm or 120-nm thickness. The absorber of 5.0,$mu$m thick is made from a Au layer and its stem is deposited in the center of the TES surface. A Ta$_{2}$O$_{5}$ insulating layer of 100-nm thickness is inserted between the overhang region of the absorber and the TES surface. A selected pixel of the TES microcalorimeter was operated for the detection of Np L X-rays emitted from an $^{241}$Am source. A response of the TES microcalorimeter to L X-rays was obtained by analyzing detection signal pulses with using the optimal filter method. An energy resolution was obtained to be 33,eV of the full width at half maximum value at 17.751,keV of Np L$_{eta 1}$ considering its natural width of 13.4,eV. Response to L X-rays emitted from a mixture source of $^{238}$Pu, $^{239}$Pu and $^{241}$Am was obtained by operating the selected pixel of the TES microcalorimeter. Major L X-ray peaks of progeny elements of $alpha$ decay of Pu and Am isotopes were clearly identified in the obtained energy spectrum. The experimental results demonstrated the separation of $^{241}$Am and plutonium isotopes by L X-ray spectroscopy.