We report on a method that allows microscopic image reconstruction from extreme-ultraviolet diffraction patterns without the need for object support constraints or other prior knowledge about the object structure. This is achieved by introducing additional diversity through rotation of an object in a rotationally asymmetric probe beam, produced by the spatial interference between two phase-coherent high-harmonic beams. With this rotational diffractive shearing interferometry method, we demonstrate robust image reconstruction of microscopic objects at wavelengths around 30 nm, using images recorded at only three to five different object rotations.