Bangkok-Shanghai-Japan-Shanghai-Beijing-Montréal

I forgot to mention that my nationality is Canadian or Portuguese (EU) and I hold both passports.

Your first stop in Shanghai is eligible for 144 hour visa free transit because you have an eligible itinerary:

Bangkok - Shanghai - Japan

Anyway, your second arrival in China, after your cruise is not eligible for 144 hour visa free transit because you plan to have two consecutive stops within mainland China (Shanghai and Beijing) and that is not allowed. You can perform such an itinerary only if your entire itinerary could be done within 24 hours.

If you want to retain actual itinerary you are supposed to obtain a Chinese tourist (L) visa in advance. If you plan to obtain your Chinese visa in Thailand, you need just a single entry visa, but you should be very focused and explain to the Chinese immigration authorities, during your first stop in China, that you will use your single entry visa after you return from the cruise and that you intend to travel on 144 hour visa free transit during your first stay in Shanghai. Otherwise, if you don't explain that upon your arrival, an immigration official could collect your single entry visa and that means that you cannot perform your intended itinerary after your cruise is over.

Thank you for the info. What is the best way to obtain a tourism visa for China in Thailand if I'm a non resident? I can't go back to Canada or Portugal (my two nationalities) but I'm a resident in the UAE and plan to go back in January. Shall I get it from there or I can still get it in Thailand? I live between Thailand and the UAE but my residency is in the UAE (with the Portuguese passport). In Thailand on a tourist visa.
Thank you

Yes, I have perfectly understood that. You are advised to apply for a Chinese visa at CVASC (Visa Application Service Center) in Dubai. You can done a lot of work online and basically just arrive there to supply them with some additional documents if needed.