Hi, I am going on a cruise from Singapore to hongkong to Xiamen to Tianjing(Beijing)

Chetan, first of all, you don't need the entry permit for HK. For your stopovers in Xiamen, Tianjin, Beijing, if the ship sails on the territorial waters of China, a single-entry G type will be enough. If it sails outside the waters of PRC, you need to apply for a multiple-entry G type. Please confirm this with the embassy.