想請教信用主咭申請破產, 銀行追討附屬咭持有人欠款？是否法律上要負責？

It depends on how the credit card agreement is written.

In most of the case, the primary cardholder will bear the full responsibility per the agreement. The supplementary cardholder will not be liable.

However - even the agreement specifies otherwise, the supplementary cardholder will only be liable of his/her own portion, not the entire outstanding balance.