Su-Wei Hsieh. No idea how to pronounce this.
As mentioned before, the mainland (Mandarin) rendering of that name would be Xie Shu-wei (pinyin) as opposed to Hsieh Su-wei (Wade/Giles). "Xie" is pronounced differently in different Mandarin dialects, but a little bit like "s(h)jeh". The initial consonant is a voiceless alveolo-palatal sibilant that doesn't exist in many languages (like English, Modern Hebrew or Eastern Arabic, but it exists in some Scandinavian languages (Dutch, Danish, Swedish - "sj")).
However, as Hsieh is not from the northern mainland, all that doesn't matter. In taiwanese Mandarin, the diphthong "Hsieh"/"Xie" is inverted in a way, not "i-eh", but "eh-(y)" and the "Hs" is often pronounced a little bit more "juicy". So basically: "shay" (with a tendency to "sheh").
Additionally, "shu" (northern mainland Mandarin) is pronounced and transcripted "su", like in southern mainland Mandarin.
If you pronounce her name "Shay Soo-way", you are pretty safe. Bonus points for correct tones, of course.