We report here on direct observation of early stages of formation of multilayered bimetallic Au-Pd core-shell nanocubes and Au-Pd-Au core-shell nanostars in liquid phase using low-dose in situ scanning transmission electron microscopy (S/TEM) with the continuous flow fluid cell. The reduction of Pd and formation of Au-Pd core-shell is achieved through the flow of the reducing agent. Initial rapid growth of Pd on Au along <111> direction is followed by a slower rearrangement of Pd shell. We propose the mechanism for the DNA-directed shape transformation of Au-Pd core-shell nanocubes to adopt a nanostar-like morphology in the presence of T30 DNA and discuss the observed nanoparticle motion in the confined volume of the fluid cell. The growth of Au shell over Au-Pd nanocube is initiated at the vertices of the nanocubes, leading to the preferential growth of the {111} facets and resulting in formation of nanostar-like particles. While the core-shell nanostructures formed in a fluid cell in situ under the low-dose imaging conditions closely resemble those obtained in solution syntheses, the reaction kinetics in the fluid cell is affected by the radiolysis of liquid reagents induced by the electron beam, altering the rate-determining reaction steps. We discuss details of the growth processes and propose the reaction mechanism in liquid phase in situ.