Pulsar Wind Nebula (PWN) DA 495 (G65.7+1.2) was detected in TeV gamma-rays by the High Altitude Water Cherenkov Observatory (HAWC) in 2017 (2HWC J1953+294). Follow-up observations by the Very Energetic Radiation Imaging Telescope Array System (VERITAS) confirmed the association between 2HWC J1953+294 and DA 495 and found the TeV emission to be spatially coincident with the radio emission first reported in 1968. The detection of TeV gamma-rays from DA 495, along with past X-ray detection up to 10 keV, prompted high energy X-ray observations as part of the NuSTAR Galactic Legacy Survey. We present the results of these NuSTAR observations, combined with archival Chandra and XMM-Newton observations, and confirm the previous X-ray photon index of Γ 2−20 keV = 2.0 ± 0.1. We find no spectral cutoff up to 20 keV. With the spectral information for DA 495 extended to TeV gamma-rays, we were able to perform analytical modeling to test leptonic and hadronic emission scenarios. The leptonic models can explain the broadband emission, but also imply a diffuse X-ray nebula of similar extent to the radio and TeV nebulae, which cannot be confirmed by our observations. The hadronic models can simultaneously explain the spectrum and the spatial extent in all wavelengths; however, we need a very high magnetic field strength pervading the radio and TeV nebulae and a surprisingly high particle kinetic energy. These requirements deepen the mystery of the physical nature of DA 495. Future observations in radio to infrared bands and spatially resolved γ-rays can further constrain the physical conditions and radiation mechanisms in DA 495.