From what I have read throughout the thread, it is much less a matter of finding him, but of making him pay the due alimonies.

There is only one way to achieve this:

A Danish court of law must enforce the claim. This is civil law and even for other EU countries, it would be difficult to enforce this outside Denmark.

As Ukraine is outside Danish / European jurisdiction, the only options are:

1) File a case through the Danish Embassy in Kiev or through a Consulate General in other cities, if feasible and eligible.

2) Go to Denmark and obtain direct enforcement plus compensation (travel expenses, cost of legal proceedings and a guarantee that alimonies will be paid). In return, however, the father has the right to see his child, even though he doesn't want to as paradoxical as it may sound. 'Renegade fathers' try to use this lever of pressure to get out of their trouble 'unscathed'.

This could lead to the following predicament: he agrees to pay alimonies in return for visits from his daughter, especially for countries with unfavourable currency conversion rates, this might prove to be difficult, unless the court of law rules that he needs to visit, if he wants to see his child.