Okay…they “want” a foreigner because they need one; the Taiwanese colleague was not able to make out what was being said on the tape accurately enough.
In the West, you could probably get $3 to $4 per typed 25-line double-spaced page of English text for doing general transcription. But you are not in the West; you’re in Taiwan, where native speakers who can type reasonably quickly and who have accurate spelling and grammar and so on are at a premium. US$3 is about NT$90+, let’s call it NT$100 per page for the sake of easier math.
A 25 line page is usually about 1 minute of tape (give or take, obviously, depending on speed, etc.) So at the very least, if you did this job for less than NT$100 x 60 minutes of tape or NT$6000 I think you would be severely underpricing yourself, and in fairness you probably deserve a higher rate because, well, if they don’t like you to earn that much money, get someone else…oh, there isn’t anyone else, is there? (Not very many, anyway.)
Six hours of work at NT$1000 per hour, if you call it NT$6000. Given that you’ve pretty much got them where you want them, if you can come up with some “good reason” (academic credentials, experience, something) you might bump it up to NT$9000 for NT$1500 per hour. Just my thoughts.
Remember, though, that there is definitely no point in doing this job for less than you could make fresh off a plane standing in front of a roomful of children saying “Apple…Banana…Carrot”. I would always compare what you’re making with the rates you could command doing other things in Taiwan (usually teaching English). A one-on-one would be paying between NT$800 and NT$1000 per hour, right? So it’s up to you which you’d prefer: typing or teaching for an hour.