Animal groups need volunteers to work shelters, walk dogs, participate in fundraisers and also foster dogs and cats (something you can do even if you are in Taiwan for a short time). Contact Taiwan Animal SOS and Taiwan SPCA.
You can also volunteer at an organic farm through WWOOF.
To work legally in Taiwan you generally need to enter on a visitor visa, have your company apply for a work permit, apply for a resident visa after you receive your work permit, and apply for an ARC after receiving your resident visa. You can apply for a visitor visa at any overseas Taiwan trade office or foreign mission. Your company applies for your work permit from the Council of Labour Affairs. You can apply for a resident visa through the Bureau of Consular Affairs. An ARC can be applied for at any office of the National Immigration Agency (www.immigration.gov.tw). For short-term employment rules see the BOCA website or visit your local Taiwan trade office or overseas mission.
Teaching English is not what it once was and there are fewer and fewer openings. Salaries have not risen in 15 years. Jobs are listed on TEALIT, Taiwanease (www.taiwanease.com), Dave's ESL Cafe (www.eslcafe.com) and plenty of other websites. If you have a teaching degree you can apply to work in a local government-run school (http://fetit.eng.ntnu.edu.tw).
If you’ve ever thought about living and working in Taiwan, then why not teach English as a foreign language (TEFL)? It could be the key to funding your travels and experiencing new cultures in a totally new way. You don’t need teaching experience or even the ability to speak the local language – although you might learn it while you’re out there.