Presented is the search for anomalous Higgs boson decays into two axion-like particles (ALPs) using the full Run 2 data set of 140 fb$^{-1}$ of proton-proton collisions at a centre-of-mass energy of 13 TeV recorded by the ATLAS experiment. The ALPs are assumed to decay into two photons, providing sensitivity to recently proposed models that could explain the $(g-2)_\mu$ discrepancy. This analysis covers an ALP mass range from 100 MeV to 62 GeV and ALP-photon couplings in the range $10^{-5}\, \text{TeV}^{-1}