We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with strongly convex regularization and general data-fit functions. We develop an inertial approach of which we analyze both convergence and stability properties. Using tools from inexact proximal calculus, we prove early stopping results with optimal convergence rates for additive data terms and further consider more general cases, such as the Kullback--Leibler divergence, for which different type of proximal point approximations hold.