The present disclosure is directed to a rotor blade for a turbomachine. The rotor blade includes an airfoil having a trailing edge surface and defining a cooling passage. The rotor blade also includes a tip shroud coupled to the airfoil. The tip shroud includes a radially inner surface. The tip shroud defines a cooling core fluidly coupled to the cooling passage. The cooling core includes at least one of a first outlet aperture having a first opening defined by the radially inner surface or a second outlet aperture having a second opening defined by the trailing edge surface of the airfoil. The first or second outlet apertures eject coolant from the cooling core in a direction of a local flow of combustion gases external to the tip shroud.