Is that possible? Taiwan->Shanghai->Frankfurt(nonstop flight , stops in Taiwan)

My flight plan is:

Taiwan to Shanghai.
Staying in Shanghai for 3 days.
Flying back to Frankfurt Germany.

but the problem is, that it is not a non-stop flight and I have to wait in Taiwan for 1h25min. So is in that case a visa needed? If yes, is there any chinese embassy in taiwan or how can I get a chinese Visa?

Thank you in Advance for helping