In this study, previously developed acetoacetates of two tall-oil-based and two commercial polyols were used to obtain polymers by the Michael reaction. The development of polymer formulations with varying cross-link density was enabled by different bio-based monomers in combination with different acrylates—bisphenol A ethoxylate diacrylate, trimethylolpropane triacrylate, and pentaerythritol tetraacrylate. New polymer materials are based on the same polyols that are suitable for polyurethanes. The new polymers have qualities comparable to polyurethanes and are obtained without the drawbacks that come with polyurethane extractions, such as the use of hazardous isocyanates or reactions under harsh conditions in the case of non-isocyanate polyurethanes. Dynamic mechanical analysis, differential scanning calorimetry, thermal gravimetric analysis, and universal strength testing equipment were used to investigate the physical and thermal characteristics of the created polymers. Polymers with a wide range of thermal and mechanical properties were obtained (glass transition temperature from 21 to 63 °C; tensile modulus (Young’s) from 8 MPa to 2710 MPa and tensile strength from 4 to 52 MPa). The synthesized polymers are thermally stable up to 300 °C. The suggested method may be used to make two-component polymer foams, coatings, resins, and composite matrices.