The use of 3D-printed components as load-bearing structures is widely studied, while their use as energy absorbers constitutes a gap in the additive manufacturing (AM) field. Most of the reported works address the compressive behavior of AM parts up to low strains (<15%), thus omitting many important properties. Therefore, this paper presents the compression characterization of Polylactic Acid (PLA) samples with different infill densities-IDs (10–100% range, with a step of 10%) fabricated by material extrusion (MEX) AM process. The physical (dimensional accuracy, printing time and sample mass) and mechanical (elastic, strength, strain and energy absorption) properties are determined and discussed in detail, along with the failure mechanisms that occur in the samples. Moreover, an ID optimization is performed based on the energy absorption diagrams (EAD), a unique approach in the AM field. The highest values of compressive strength (81 MPa) and modulus (1306.6 MPa) are found for 90%-ID, over 2.2% higher than those obtained for 100%-ID. On the other hand, based on three different approaches, EAD identified 30%-ID as optimal. The 30%-ID samples absorb the largest amount of energy (12 MJ/m3) at the lowest (ideal) peak stress value (23.57 MPa), which is 69.1% lower than that for 100%-ID. At low IDs (<30%), the samples exhibit a brittle behavior, changing to a ductile one with the increase of ID (≥40%). The MEX-printed PLA samples show a dimensional relative error below 0.15%, and the optimization process reduces the amount of filament material by 54.3% and the printing time by 42.7%.