We demonstrate the self-supporting 3D printing of complex hydrogel structures based on simultaneous crosslinking reactions while printing. The printing strategy is based on the Schiff base reaction and metal coordination with a two-step crosslinking process. The printing ink was first prepared by dispersing oxidized sodium alginate (OSA) and adipic dihydrazide (ADH) in poly(acrylamide-co-acrylic acid) (P(AAm-co-AAc)) polymer solutions, and was mixed and printed into 3D structures with an extrusion-based coaxial printing platform. Because of the rapid chemical crosslinking reaction between the aldehyde group in OSA and the hydrazide group in ADH, the printed structures can be solidified quickly, and are further crosslinked by forming carboxyl-Fe3+ coordination complexes to enhance their mechanical properties. The dynamic time-sweep rheological properties of the gel composed of different proportions of OSA and ADH were systematically investigated for the characteristic gelation time, and compression tests were carried out to measure the mechanical properties of the gel composed of OSA and ADH. Combining the gelation time and mechanical properties of the gel, the weight ratio of OSA and ADH was selected as 1 : 0.44 for an optimized setting in the subsequent printing. To evaluate the printability of inks, the material formula and printing parameters were systematically varied. The ink exhibited a wide printing range, self-supporting properties, and good printability. Tensile tests of the printed single fiber crosslinked by Fe3+ show that its strength and toughness are tunable. Complex 3D structures such as pyramids, cylinders, and noses were constructed to demonstrate the printability of the ink. This printing method provides a facile approach for tough hydrogel fabrication without changing the rheological properties of the ink or sacrificing the ultimate mechanical properties of the printed materials.