A certificate of no impedance to marry( certificate of freedom to marry) issued from the relevant authority in Denmark, and stamped by the Taiwan office in Denmark, is required
Perhaps if he is not in Denmark, he should contact the Danish embassy in the country he is currently residing in to get it issued from there.
However the Taiwan authorities would still want it stamped in the Taiwan office in Denmark, and you may be forced to go the extra step of getting it stamped in the Ministry of Foreign Affairs of Denmark in Denmark before they will stamp it in the Taiwan office.
Different countries have different ways of issuing certs either through the local registrar of department of foreign affairs. In some cases there are waiting times and residency requirements. Your boyfriend should get in contact with the Danish Authoritries to check the requirements