Embedded 3D printing is widely adapted for fabricating architected soft and non-self-supporting hydrogels for applications ranging from tissue engineering to soft robotics. Although the matching between hydrogels and supportive baths sets the foundation in embedded 3D printing, the rule-of-thumb for supportive bath selection and creation is not yet established. Herein, the “shapeability” of distinct classes of hydrogel inks (i.e., pH-responsive, photo-crosslinkable, thermal-sensitive, chemically crosslinkable monomeric, and cationic and anionic inks) in diverse representative support baths (i.e., gelatin slurry, agarose fluid gel, Carbopol and oil-based baths) is evaluated. The results show that the dominate mechanisms for interfacial instabilities, including diffusion-driven or charge-driven, can be predicted by evaluating the composition pairing of the pre-crosslinked hydrogel ink and supportive bath. Based on this, a general and simplistic guideline for supportive bath selection to attain hydrogel shapeability is proposed. The approach can widen the spectrum of hydrogel materials that can be structured on-demand for a plethora of functionalities.