Axion-like particles (ALPs), a class of pseudoscalars common to many extensions of the Standard Model, have the capacity to drain energy from the interiors of stars. Consequently, stellar evolution can be used to derive many constraints on ALPs. We study the influence that keV-MeV scale ALPs which interact exclusively with photons can exert on the helium-burning shells of asymptotic giant branch stars, the late-life evolutionary phase of stars with initial masses less than $8M_{odot}$. We establish the sensitivity of the final stellar mass to such energy-loss for ALPs with masses currently permitted by stellar evolution bounds. A semi-empirical constraint on the white dwarf initial-final mass relation (IFMR) derived from observation of double white dwarf binaries is then used to exclude part of a currently unconstrained region of ALP parameter space, the cosmological triangle. The derived constraint relaxes when the ALP decay length becomes shorter than the width of the helium-burning shell. Other potential sources for stellar constraints on ALPs are also discussed.