Dendrites are typical microstructures formed during the solidification of metal alloys. Dendritic microstructures directly impact the mechanical properties of casting products. Therefore, an accurate evaluation of the evolution of dendritic patterns is essential. Among numerical approaches, the phase-field (PF) method is the most powerful simulation tool for predicting dendrite growth. However, obtaining accurate material parameters for inputting into PF simulations is challenging. Among the typically used experimental approaches, time-resolved X-ray computed tomography is the most powerful method for the prediction of dendrite growth. However, the low spatio-temporal resolution of this method is an issue that must be addressed, especially for fast phenomena. Hence, combining PF simulations and X-ray tomography is a promising strategy for simultaneously solving these problems. The data assimilation technique, which was originally used in the fields of meteorology and oceanography, can enable the combination of the aforementioned two approaches. Recently, we developed data assimilation systems for dendrite growth with melt convection and for directional solidification. In this study, we developed a system for achieving high-accuracy data assimilation of the dendrite growth in a binary alloy. To validate the developed data assimilation system, we performed twin experiments to simultaneously estimate the material parameters, crystal orientation, high-resolution dendrite morphology, and solute concentration distribution. The results showed that the developed system can simultaneously solve the problems of simulations and experiments and improve the prediction accuracy of dendrite growth.