We demonstrated a class of highly nonlinear hybrid waveguide structures based on infiltration of As2S3 chalcogenide glass into silicon slot waveguides. The nonlinear properties of the hybrid waveguides were precisely quantified via a bidirectional top-hat D-scan method, enabling a direct comparison between properties measured using different device geometries. We experimentally demonstrate hybrid As2S3-Si slot waveguides with a two-photon absorption (TPA) figure of merit exceeding 2 at near infrared wavelengths. These waveguides largely satisfy the critical criterion for efficient nonlinear integrated photonics (FOMTPAwg>1), allowing phase shifts greater than π with minimal overall losses. These results pave the way for efficient and robust ultrafast all-optical devices and circuits in large-scale silicon photonics technology.