We identify sources with extremely hard X-ray spectra (i.e., with photon indices of G 0.6) in the 13deg 2 NuSTAR serendipitous survey, to search for the most highly obscured active galactic nuclei (AGNs) detected at >10 keV. Eight extreme NuSTAR sources are identified, and we use the NuSTAR data in combination with lower-energy X-ray observations (from Chandra, SwiftXRT, and XMM-Newton) to characterize the broadband (0.5-24 keV) X-ray spectra. We find that all of the extreme sources are highly obscured AGNs, including three robust Compton-thick (CT; >Ń 1.5 10 H 24 cm −2 ) AGNs at low redshift ( < z 0.1) and a likely CT AGN at higher redshift (z = 0.16). Most of the extreme sources would not have been identified as highly obscured based on the low-energy (<10 keV) X-ray coverage alone. The multiwavelength properties (e.g., optical spectra and X-ray-mid-IR luminosity ratios) provide further support for the eight sources being significantly obscured. Correcting for absorption, the intrinsic rest-frame 10-40keV luminosities of the extreme sources cover a broad range, from »5 10 42 to 10 45 erg s −1 . The estimated number counts of CT AGNs in the NuSTAR serendipitous survey are in broad agreement with model expectations based on previous X-ray surveys, except for the lowest redshifts ( < z 0.07), where we measure a high CT fraction of16 . For the small sample of CT AGNs, we find a high fraction of galaxy major mergers (50% ± 33%) compared to control samples of "normal" AGNs.