The X-ray emission from active galactic nuclei is believed to come from a combination of inverse Compton scattering of photons from the accretion disk and reprocessing of the direct X-ray emission by reflection. We present hard (10–80 keV) and soft (0.5–8 keV) X-ray monitoring of a gravitationally lensed quasar RX J1131−1231 (hereafter RXJ1131) with NuSTAR, Swift, and XMM-Newton between 2016 June 10 and 2020 November 30. Comparing the amplitude of quasar microlensing variability at the hard and soft bands allows a size comparison, where larger sources lead to smaller microlensing variability. During the period between 2018 June 6 and 2020 November 30, where both the hard and soft light curves are available, the hard and soft bands varied by factors of 3.7 and 5.5, respectively, with rms variability of 0.40 ± 0.05 and 0.57 ± 0.02. Both the variability amplitude and rms are moderately smaller for the hard X-ray emission, indicating that the hard X-ray emission is moderately larger than the soft X-ray emission region. We found the reflection fraction from seven joint hard and soft X-ray monitoring epochs is effectively consistent with a constant with low significance variability. After decomposing the total X-ray flux into direct and reprocessed components, we find a smaller variability amplitude for the reprocessed flux compared to the direct emission. The power-law cutoff energy is constrained at keV, which positions the system in the allowable parameter space due to the pair production limit.