Three-dimensional (3D) bio-printing has recently emerged as a crucial technology in tissue engineering, yet there are still challenges in selecting materials to obtain good print quality. Therefore, it is essential to study the influence of the chosen material (i.e., bio-ink) and the printing parameters on the final result. The "printability" of a bio-ink indicates its suitability for bio-printing. Hydrogels are a great choice because of their biocompatibility, but their printability is crucial for exploiting their properties and ensuring high printing accuracy. However, the printing settings are seldom addressed when printing hydrogels. In this context, this study explored the printability of double network (DN) hydrogels, from printing lines (1D structures) to lattices (2D structures) and 3D tubular structures, with a focus on printing accuracy. The DN hydrogel has two entangled cross-linked networks and a balanced mechanical performance combining high strength, toughness, and biocompatibility. The combination of poly (ethylene glycol)-diacrylate (PEDGA) and sodium alginate (SA) enables the qualities mentioned earlier to be met, as well as the use of UV to prevent filament collapse under gravity. Critical correlations between the printability and settings, such as velocity and viscosity of the ink, were identified. PEGDA/alginate-based double network hydrogels were explored and prepared, and printing conditions were improved to achieve 3D complex architectures, such as tubular structures. The DN solution ink was found to be unsuitable for extrudability; hence, glycerol was added to enhance the process. Different glycerol concentrations and flow rates were investigated. The solution containing 25% glycerol and a flow rate of 2 mm/s yielded the best printing accuracy. Thanks to these parameters, a line width of 1 mm and an angle printing inaccuracy of less than 1° were achieved, indicating good shape accuracy. Once the optimal parameters were identified, a tubular structure was achieved with a high printing accuracy. This study demonstrated a 3D printing hydrogel structure using a commercial 3D bio-printer (REGEMAT 3D BIO V1) by synchronizing all parameters, serving as a reference for future more complex 3D structures.