Thanks for your question.
Normally, a Taiwanese citizen traveling from Taiwan will not require a visa prior to traveling and will receive a visa upon port of entry (ie. at customs). This is discretionary however which means that the customs officials can refuse a visa if they wish. This will usually be on grounds of suspecting the person(s) are entering for the purpose of actually staying for longer than the 6 month period permitted under the visa or because of suspected criminal activity.
You can check this here:-
Visitors who do not wish to take that risk can apply for a 6 month visitor's visa to their nearest British Embassy prior to traveling. She would have to show that she intends to return home before the expiry of the 6 month period, that she does not intend to undertake paid or unpaid work whilst she is here and that she has enough money to support herself whilst she is here without the need to access public funds.
Such evidence would be her evidence of her job/accommodation in Taiwan that she intends to return (eg. statements from her others, documentary evidence of job/accommodation). Bank statements to evidence the money she has available. You could also write a letter of invitation stating that you are to provide her with a place to stay whilst she is here free of charge and will also assist in the case of emergency if extra funds are required.
I attach a link to the UK visas page for such a visa:-
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