We explore the impact of additive noise on phase transitions in a predator-prey system, which is formulated by stochastic partial differential equations (SPDEs). The system is observed to experience twice phase transitions under certain level of additive noise. We extend the multiple scaling approach from single SPDE to multiple SPDEs and find a necessary and sufficient condition to excite the occurrence of the first transition from a spatially homogeneous state to a spatially regular spiral wave. Numerical experiments show the second phase transition from the regular spatial pattern to spiral turbulence. We conclude that additive noise has a destabilising effect on population dynamics by triggering the onset of Hopf bifurcation.