Taiwan - Shanghai - Hong Kong

Yes you do.

Thank you for your response. We are flying EVA Airlines Toronto - Taiwan and direct to Shanghai. The check in staff at the airport have said we do NOT qualify for the 144 Transit without visa as you need to enter/exit via the same mode eg. air. We interpret the policy that we can enter/exit as noted via air/vessel/train in ….is there anything more specific we can provide the airline?

The staff is wrong. Tell them to carefully consult Timatic and/or call Shanghai immigration (they also have a website). You should be eligible if your first port of call after Shanghai is outside Mainland China. If this caused you to miss your cruise you should seek monetary compensation by filing a formal complaint to the government of your country of residence or through the court system.