We present a flyscan compatible acquisition scheme for three-modal X-Ray Computed Tomography (CT) with two-dimensional phase sensitivity. Our approach is demonstrated using a “beam tracking” setup, through which a sample’s attenuation, phase (refraction) and scattering properties can be measured from a single frame, providing three complementary contrast channels. Up to now, such setups required the sample to be stepped at each rotation angle to sample signals at an adequate rate, to prevent resolution losses, anisotropic resolution, and under-sampling artefacts. However, the need for stepping necessitated a step-and-shoot implementation, which is affected by motors’ overheads and increases the total scan time. By contrast, our proposed scheme, by which continuous horizontal and vertical translations of the sample are integrated with its rotation (leading to a “cycloidal-spiral” trajectory), is fully compatible with continuous scanning (flyscans). This leads to greatly reduced scan times while largely preserving image quality and isotropic resolution.