The development of biobased polyesters with the combination of high UV shielding and degradability is a significant challenge. Herein, three 4-membered cyclic monomers containing two pyrrolidone and two furan rings were prepared by the aza-Michael addition of biobased bifuran diamine and dimethyl itaconate (DMI). They were available in melt polycondensation reactions with various diols to synthesize biobased polyesters. The bifuran structure endowed the polyesters with ultrahigh UV-shielding cutoff values of up to 443 nm, which achieved the highest UV-shielding results among the commercial polyesters. The bipyrrolidone structure conferred high hydrolysis sensitivity to the polyesters, which facilitated hydrolytic degradation of the polyester in an aqueous environment. The variability of the link structure between the multirings of the three monomers can regulate the various properties of the polyesters. Overall, the 4-membered cyclic monomers are promising precursors for sustainable biobased materials in providing high UV shielding and hydrolysis sensitivity.