In this work, the evolution of the dislocations microstructure in single crystal two-phase superalloy microcrystals under monotonic loading has been studied using the three-dimensional discrete dislocation dynamics (DDD) method. The DDD framework has been extended to properly handle the collective behavior of dislocations and their interactions with large collections of arbitrary shaped precipitates. Few constraints are imposed on the initial distribution of the dislocations or the precipitates, and the extended DDD framework can support experimentally-obtained precipitate geometries. Full tracking of the creation and destruction of anti-phase boundaries (APB) is accounted for. The effects of the precipitate volume fraction, APB energy, precipitate size, and crystal size on the deformation of superalloy microcrystals have been quantified. Correlations between the precipitate microstructure and the dominant deformation features, such as dislocation looping versus precipitate shearing, are also discussed. It is shown that the mechanical strength is independent of the crystal size, increases linearly with increasing the volume fraction, follows a near square-root relationship with the APB energy and an inverse square-root relationship with the precipitate size. Finally, the flow strength in simulations having initial dislocation pair sources show a flow strength that is about one half of that predicted from simulations starting with single dislocation sources. The method developed can be used, with minimal extensions, to simulate dislocation microstructure evolution in general multiphase materials.