Is there any way someone in Taiwan can transfer money to me in Singapore?

You can try Transfernow which is base on how much you transfer as well as ot has better exchange rates which I have used so far. It is cheaper than M1 Remit and safe too. Transfer can be done with USD and other currencies but not in Taiwan dollars.

But in order to prevent money laundering, it has some step by step security features to follow.

You can use my referral code below to get a free transfer for the first time:

https://transferwise.com/invite/a/leel364

Let me know if you have any question. :)

Cheers.

Stuart

The most straightforward way will be via telegraphic transfer. However, there is likely to be some bank charges involved.