Visa free 144 hour

Actually, you will apply for a temporary entry permit based on your 144 hour visa free transit eligibility upon your arrival in Tianjin (Beijing). Also, it is possible that some of the paperwork will be done on board the ship, but this depends on several circumstances, in the first place about the cooperation between the cruise company and the Chinese immigration authorities. Never mind, you should have your flight ticket for Beijing to Singapore route printed out and ready to be presented to the Chinese immigration authorities. This is essential and you really don't need to procure any additional documentation because your itinerary:

Japan - Beijing - Singapore

Is definitely eligible for 144 hour visa free transit in Beijing area. In other words, you will start mentioning this option only in Japan because there you will have your last port of call, immediately before Tianjin (Beijing). You will almost for certain be asked about your intentions by Japanese authorities and you will tell them that you will travel to Singapore via Beijing using 144 hour visa free transit. You will present them your flight ticket and you will be allowed to proceed by your cruise to Tianjin (Beijing).