We consider dominant strategy implementation in a large population aggregative game. The model has strategic complementarities which generates multiple Nash equilibria. Moreover, externalities are positive due to which, all equilibria are socially inefficient. The planner, therefore, constructs a direct mechanism and assigns efficient strategies and transfer levels to agents. Truthful revelation then becomes strictly dominant, which implements efficiency. In our new evolutionary approach to this mechanism, the reported type distribution evolves under dynamics satisfying monotone percentage growth. Such dynamics eliminate dominated strategies thereby ensuring convergence to truthful revelation by all agents. Dominant strategy implementation is, therefore, robust under such evolutionary dynamics. Our evolutionary approach differs from existing models of evolutionary implementation based on potential games. That approach may fail to implement efficiency under strategic complementarities as a Pareto inferior Nash equilibrium can remain asymptotically stable under evolutionary dynamics. Our evolutionary approach is effective even under such strategic complementarities.