Few-photon optical nonlinearity in planar solid-state systems is challenging yet crucial for quantum and classical optical information processing. Polaritonic nonlinear metasurfaces have emerged as a promising candidate to push the photon number down -- but have often been hindered by challenges like the poor photon-trapping efficiency and lack of modal overlap. Here, we address these issues in a self-hybridized perovskite metasurface through critical coupling engineering, and report strong polaritonic nonlinear absorption at an ultra-low incident power density of only 519 W/cm2 (2 orders of magnitude lower than the state of art in free-space planar devices), with an estimated photon number of 6.12 per cavity lifetime. Taking advantage of a quasi-bound-state-in-the-continuum design with asymmetry-controlled quality-(Q)-factor, we systematically examine the Q-dependent device nonlinearity and determine the optimal cavity critical coupling condition. With the optimized device, we demonstrate at 6 Kelvin a tunable nonlinear response from reverse saturable absorption to saturable absorption at varying pump powers, with a maximal effective nonlinear absorption coefficient up to 29.4+-5.8 cm/W (6 orders of magnitude larger than unpatterned perovskites) at 560 nm wavelength. In addition, the cavity-exciton detuning dependent device response is analyzed and well explained by a phase-space-filling model, elucidating the underlying physics and the origin of giant nonlinearity. Our study paves the way towards practical flat nonlinear optical devices with large functional areas and massive parallel operation capabilities.