  We present evidence of diffuse, non-thermal X-ray emission from the
superbubble 30 Doradus C (30 Dor C) using hard X-ray images and spectra from
NuSTAR observations. For this analysis, we utilize data from a 200 ks targeted
observation of 30 Dor C as well as 2.8 Ms of serendipitous off-axis
observations from the monitoring of nearby SN 1987A. The complete shell of 30
Dor C is detected up to 20 keV, and the young supernova remnant MCSNR
J0536-6913 in the southeast of 30 Dor C is not detected above 8 keV.
Additionally, six point sources identified in previous Chandra and XMM-Newton
investigations have hard X-ray emission coincident with their locations. Joint
spectral fits to the NuSTAR and XMM-Newton spectra across the 30 Dor C shell
confirm the non-thermal nature of the diffuse emission. Given the best-fit
rolloff frequencies of the X-ray spectra, we find maximum electron energies of
70-110 TeV (assuming a B-field strength of 4$\mu$G), suggesting 30 Dor C is
accelerating particles. Particles are either accelerated via diffusive shock
acceleration at locations where the shocks have not stalled behind the
H$\alpha$ shell, or cosmic-rays are accelerated through repeated acceleration
of low-energy particles via turbulence and magnetohydrodynamic waves in the
bubble's interior.
