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 $1.7\mathrm{\mu m}$ and produces a synchrotron spectrum with critical energy $E_c=12.3\pm 2.5\mathrm{keV}$ and ${10}^9$ photons per shot in the whole spectrum.