Here is an official government list of immigration consultants in Taiwan. The list has 279 firms on it. This firms are licensed as immigration consultants. (By law, this license is required.)
The name of the document is 合法設立並領取註冊登記證移民公司
I believe most of them specialize in immigration out of Taiwan to another country. But some of them work on immigration to Taiwan.
You can use this search below, provided by tando, to find firms and then check that the firm is licensed.
tando’s search: (thank you to tando!)
I used google with these words.
無戶籍國民 國際移民 代辦 -site:gov.tw -site:edu.tw
This search turns up similar results. You can also use this search
移民顧問 移民台灣 無戶籍國民 -gov.tw