Au and Ag atoms have different electron density, which should provide sufficient contrast to distinguish the Au core and Ag shell. Hence, you can do HR-TEM analysis.

You can use XRD, XPS, TEM, HRTEM, electron diffraction (SAED) for core-shell structure determination AuAg bimetallic nanoparticles.

Do line scans using FESEM on a magnified nanoparticle from its one end to another end. Do elemental mapping along the line.