We study the general chaotic features of dynamics of a phantom field modelled in terms of a single scalar field conformally coupled to gravity. We demonstrate that the dynamics of the Friedmann–Robertson–Walker model with dark energy in the form of a phantom field can be regarded as a scattering process of either multiple chaotic or classical non-chaotic type, depending on whether spontaneous symmetry breaking takes place. For the first class of models with spontaneous symmetry breaking, the dynamics is similar to that of the Yang–Mills theory. We find evidence for a fractal structure in the phase space of initial conditions. We observe similarities to the phenomenon of a multiple scattering process around the origin. The class of models without spontaneous symmetry breaking can be described as classical non-chaotic scattering processes and the methods of symbolic dynamics are also used in this case. We show that the phantom cosmology can be treated as a simple model with scattering of trajectories whose character depends crucially on the sign of the square of the mass. We demonstrate that there is a possibility of chaotic behaviour in the flat Universe with a conformally coupled phantom field in the system considered on the non-zero energy level. We obtain that the acceleration is a generic feature in the model considered, without spontaneous symmetry breaking. We observe that the effective equation of state coefficient oscillates and then approaches w = −1.