Light-mediated polymer degradation has attracted considerable attention in various applications, including photo-patterning, tissue engineering and photo-triggered drug delivery. In this study, we report the synthesis and characterization of a new, linear, main-chain photo- and acid-degradable copolymer based on acylhydrazone linkages. The polymer was synthesized via a step-growth copolymerization of adipic acid dihydrazide with a bifunctional poly(ethylene glycol) bearing benzaldehyde end-groups, under mild acidic conditions, to afford a hydrophilic PEG-alt-adipic acid (PEG-alt-AA) alternating copolymer. The synthesized polymer was characterized by size exclusion chromatography, proton nuclear magnetic resonance and attenuated total reflection-Fourier transform infrared spectroscopies. The main-chain photo- and acid-induced degradation of the copolymer in dimethylsulfoxide and water, respectively, was verified by UV-vis spectroscopy at light intensities as low as 0.1 mW cm−2 at λ = 254 nm. Next, a model anticancer drug, doxorubicin (DOX), was chemically linked to the polymer chain end(s) via acylhydrazone bond(s), resulting in amphiphilic PEG-alt-adipic acid-DOX (PEG-alt-AA-DOX) polymer–drug conjugates. The conjugates were self-assembled in water to form spherical nanoparticles, as evidenced by scanning and transmission electron microscopies. The irradiation of the self-assembled PEG-alt-AA-DOX conjugates with UV light and the decrease of the solution pH resulted in the disruption of the assemblies due to the photolysis and acidolysis of the acylhydrazone bonds, and the release of the therapeutic cargo.