Self-assembling hydrogels are promising materials for regenerative medicine and tissue engineering. However, designing hydrogels that replicate the 3-4 order of magnitude variation in soft tissue mechanics remains a major challenge. Here hybrid hydrogels are investigated formed from short self-assembling -fibril peptides, and the glycosaminoglycan chondroitin sulfate (CS), chosen to replicate physical aspects of proteoglycans, specifically natural aggrecan, which provides structural mechanics to soft tissues. Varying the peptide:CS compositional ratio (1:2, 1:10, or 1:20) can tune the mechanics of the gel by one to two orders of magnitude. In addition, it is demonstrated that at any fixed composition, the gel shear modulus can be tuned over approximately two orders of magnitude through varying the initial vortex mixing time. This tuneability arises due to changes in the mesoscale structure of the gel network (fibril width, length, and connectivity), giving rise to both shear-thickening and shear-thinning behavior. The resulting hydrogels range in shear elastic moduli from 0.14 to 220 kPa, mimicking the mechanical variability in a range of soft tissues. The high degree of discrete tuneability of composition and mechanics in these hydrogels makes them particularly promising for matching the chemical and mechanical requirements of different applications in tissue engineering and regenerative medicine.