One-dimensional Airy beams allow the generation of thin light-sheets without scanning, simplifying the complex optical arrangements of light-sheet microscopes (LSMs) with an extended field of view (FOV). However, their uniaxial acceleration limits the maximum numerical aperture of the detection objective in order to keep both the active and inactive axes within the depth of field. This problem is particularly pronounced in miniaturized LSM implementations, such as those for endomicroscopy or multi-photon neural imaging in freely moving animals using head-mounted miniscopes. We propose a new method to generate a static Airy light-sheet with biaxial acceleration, based on a novel phase profile. This light-sheet has the geometry of a spherical shell whose radius of curvature can be designed to match the field curvature of the micro-objective. We present an analytical model for the analysis of the light-sheet parameters and verify it by numerical simulations in the paraxial regime. We also discuss a micro-optical experimental implementation combining gradient-index optics with a 3D-nanoprinted, fully refractive phase plate. The results confirm that we are able to match detection curvatures with radii in the range of 1.5 to 2 mm.