You need to submit following documents to Chinese embassy there in Tokyo on their working days:
1. a valid passport valid at least 6 months with 2 blank visa pages;
2. One passport photo;
3. An application form for PRC;
4. Your re-entry permit to Japan;
The general processing time is 4 working days, and there are express and rush service available, you need to pay extra service fee if you want to use any.

For the re-entry permit to Japan, do I only need to have multiple-entry visa to Japan in my passport? or do I also need to submit/show my alien card? I just consider if I can go to Chinese Embassy on the same day when I will the new extension visa from the immigration office in Tokyo. Thank you!

The multiple-entry visa to Japan on your passport or the alien card are both Ok to prove that you can return to Japan legally.