High-density polyethylene (HDPE) is a light and low-cost polymer widely explored as an excellent barrier material for γ-ray and neutron radiation in situations of high exposure (e.g., aerospace). Nevertheless, this polymer is not a suitable structural material due to its low mechanical resistance. Herein, amino-functionalized carbon nanotubes (CNTs) and graphene oxide (GO) were incorporated into HDPE and statistically studied through a Taguchi design of experiments (DoE) model that investigated their synergistic effect. After incorporating these nanocarbons, microscopy images suggest their homogeneous distribution into HDPE. Furthermore, X-ray diffraction shows that the HDPE crystallinity degree increased due to a nucleation effect caused by the nanofillers. Additionally, all nanocomposites presented improved microhardness resistance (up to 69%), particularly when both nanocarbons were incorporated into the matrix. The nanocomposite with higher microhardness resistance had the γ-ray attenuation potential, exhibiting a similar radiation shielding effect to HDPE, with a linear attenuation coefficient higher than Aluminum, a reference material. Hence, this study shows that the synergy between these nanocarbons can be explored to improve HDPE hardness without negatively affecting its attenuation ability. Therefore, these nanocomposites with improved hardness and γ-ray shielding are potential materials for applications requiring surface durability and radiation resistance, such as in air-/spacecraft systems.