Scholarships to select universities -NTU, NTNU, Suna Yat Sen, Cheng Kong, Hsin Hua, and Chengda- are quite competitive. Not impossible so, but remember there are always alternatives, from full scholarship plus benefits, up to paying half price tuition. So, if you do not get the top one, you still have opportunity for others, up to a discount. Remember, aside from MOFA and MOE, each university has funds to provide scholarships.
Insurance is not a hidden cost, but it should also be factores. Usually, you pay a whole semester with your tuition. Many universities have “miscelaneous fees” -lab and library use, maintenance, whatever- and those mount up to 5 to 10 thousand NTs, depending on the school.
Are you bringing your own computer or buying it here? Remember to bring clothes for all 4 seasons, but a winter jacket is best bought here -different materials for humid weather. You might need to buy a mattress, unless you are already used to sleeping on the floor or a similarly hard surface. You also might need to buy a fan in summer and a small heater in winter, cheap and very, very useful.
The lion’s share of your budget will be housing and food. Decide ahead where you want to live -dorm or outside- and factor the pricing accordingly. Same with food. Local is cheap, foreign starts to add up -poundwise and moneywise.