The primary purpose of this work was to design and obtain a series of curcuminoid chalcone–NSAID hybrid derivatives. The ester-type hybrid compounds with ibuprofen (i), ketoprofen (ii), and naproxen (iii) were obtained in two ways, using the Claisen–Schmidt reaction and the Steglich esterification reaction. The designed molecules were successfully synthesised, and FT-IR, MS, and NMR spectroscopy confirmed their structures. Moreover, the cytotoxic effect of the sonodynamic therapy and the anti-inflammatory, antioxidant, and anticholinergic properties of some curcuminoid chalcones and curcuminoid chalcones hybrids were evaluated. The curcuminoid chalcone derivatives showed promising neuroprotective activity as sonosensitisers for sonodynamic therapy in the studied cell lines. Additionally, the stability of the ester-type hybrid compounds with promising activity was determined. The RP-HPLC method was used to observe the degradation of the tested compounds. Studies have shown that structural isomers of ester-type hybrid compounds (3ai, 3bi) are characterised by a similar susceptibility to degradation factors, i.e., they are extremely unstable in alkaline environments, very unstable in acidic environments, unstable in neutral environments, practically stable in oxidising environments, and photolabile in solutions and in the solid phase. These compounds maintain adequate stability in environment at pH 1.2 and 6.8, which may make them good candidates for developing formulations for oral administration.