We consider a one-dimensional microscopic reaction-diffusion process obtained as a superposition of a Glauber and a Kawasaki dynamics. The reaction term is tuned so that a dynamical phase transition occurs in the model as a suitable parameter is varied. We study dynamical fluctuations of the particle's density at the critical point. We characterise the slowdown of the dynamics at criticality, prove that density fluctuations are non-Gaussian and characterise their limit as the solution of a non-linear SDE. The proof relies on a decoupling of slow and fast scales relying in particular on a relative entropy argument. Joint work with Benoit Dagallier.