Achromatic quarter waveplates (A-QWPs), traditionally constructed from multiple birefringent crystals, can modulate light polarization and retardation across a broad range of wavelengths. This mechanism is inherently related to phase retardation controlled by the fast and slow axis of stacked multi-birefringent crystals. However, the conventional design of A-QWPs requires the incorporation of multiple birefringent crystals, which complicates the manufacturing process and raises costs. Here, we report the discovery of a broadband (540-1060 nm) A-QWP based on a two-dimensional (2D) layered hybrid copper halide (HCH) perovskite single crystal. The 2D copper chloride (CuCl6) layers of the HCH crystal undergo Jahn-Teller distortion and subsequently trigger the in-plane optical birefringence. Its broad range of the wavelength response as an A-QWP is a consequence of the out-of-plane mosaicity formed among the stacked inorganic layers during the single-crystal self-assembly process in the solution phase. Given the versatility of 2D hybridhalide perovskites, the 2D HCH crystal offers a promising approach for designing cost-effective A-QWPs and the ability to integrate other optical devices.