We are going to Singapore for four days then Beijing for three days

Actually, you don't need a visa at all. During your first stay in Beijing, you will be eligible for 144 hour visa free transit because of your itinerary:

Singapore - Beijing - Japan

During your second arrival in Beijing, your short transit will be covered by 24 hour visa free transit.

Here are just a couple of conditions your itinerary has to fulfill to be really and definitely eligible for the mentioned visa free transit options:

- All your flights to and from Beijing should not have any additional landing within mainland China
- Your cruise is not allowed to have its first port of call, immediately after Tianjin (Beijing), in mainland China

If the above conditions are fulfilled, you are definitely eligible for visa free transit in Beijing twice.