Development of x-ray phase contrast imaging applications with a laboratory scale source have been limited by the long exposure time needed to obtain one image. We demonstrate, using the Betatron x-ray radiation produced when electrons are accelerated and wiggled in the laser-wakefield cavity, that a high-quality phase contrast image of a complex object (here, a bee), located in air, can be obtained with a single laser shot. The Betatron x-ray source used in this proof of principle experiment has a source diameter of 1.7 μm and produces a synchrotron spectrum with critical energy E(c)=12.3±2.5 keV and 10⁹ photons per shot in the whole spectrum.