Described herein are apparatuses, systems, and methods for fabricating tissue constructs, such as by fabricating perfusable tissue constructs by embedding a sacrificial material into a composite matrix yield stress support bath. A composite matrix bath can include a microgel filler and a hydrogel precursor. An extrusion tip can be used for embedded printing of perfusable tissue constructs by disposing sacrificial material into the composite matrix bath while the extrusion tip travels along a predefined course through the composite matrix bath. This sacrificial material can be the printed tissue construct or can be removed to render the matrix bath a perfusable tissue construct. The composite matrix bath can include acellular or cell-laden hydrogels. The sacrificial material can include a salt and a physiological buffer or a non-cytotoxic porogen material. The hydrogel precursor can include at least one of gellan and gelatin. Cross-linking can be carried out chemically, thermally, enzymatically, or physically.