Air tightness is a challenging task for 3D-printed components, especially for fused filament fabrication (FFF), due to inherent issues, related to the layer-by-layer fabrication method. On the other hand, the capability of 3D print airtight cavities with complex shapes is very attractive for several emerging research fields, such as soft robotics. The present paper proposes a repeatable methodology to 3D print airtight soft actuators with embedded air connectors. The FFF process has been optimized to manufacture monolithic bending PneuNets (MBPs), an emerging class of soft robots. FFF has several advantages in soft robot fabrication: (i) it is a fully automated process which does not require manual tasks as for molding, (ii) it is one of the most ubiquitous and inexpensive (FFF 3D printers costs < $200) 3D-printing technologies, and (iii) more materials can be used in the same printing cycle which allows embedding of several elements in the soft robot body. Using commercial soft filaments and a dual-extruder 3D printer, at first, a novel air connector which can be easily embedded in each soft robot, made via FFF technology with a single printing cycle, has been fabricated and tested. This new embedded air connector (EAC) prevents air leaks at the interface between pneumatic pipe and soft robot and replaces the commercial air connections, often origin of leakages in soft robots. A subsequent experimental study using four different shapes of MBPs, each equipped with EAC, showed the way in which different design configurations can affect bending performance. By focusing on the best performing shape, among the tested ones, the authors studied the relationship between bending performance and air tightness, proving how the Design for Additive Manufacturing approach is essential for advanced applications involving FFF. In particular, the relationship between chamber wall thickness and printing parameters has been analyzed, the thickness of the walls has been studied from 1.6 to 1 mm while maintaining air tightness ...