Which Visa Do We Need Please

In October we are flying from Heathrow to Beijing then Beijing to Xi'an (same day) 6days for tours etc including bullet train back to Beijing - We then board cruise ship in Beijing for 12 nights visiting Japan, Taipei, Hong Kong, Hue/Danang, Nha Trang, Ho Chi Minh, Singapore. We then fly from Singapore to Beijing- Beijing to Heathrow (2hr wait in Beijing). Many thanks.....