Pakistan does have some kind of civil wedding system and also a requirement to register marriages but it also recognises unregistered religious ceremonies (Islamic ones anyway) as valid marriages so even if he had a religious ceremony, he is married under Pakistani law and therefore he was not free to contract a marriage in Ireland. So, if you could obtain some proof, you would have a chance of getting the Irish marriage declared void.
Would any of his friends know the name of the wife or any other details that they'd be prepared to give you? If there's a child the birth would surely have been registered. What city is he from? How old would the child be? If you're really determined, you could start to piece together some information and then go to a solicitor and see what the chances are. In the meantime you could get the forms for voiding a marriage from the courts and see what information you need to provide.
It might be a good idea to put the fear of God in him by bluffing that you have 'certain proof' which you have obtained and that he has a choice to agree to divorce in Poland or you will take steps to apply to the Irish courts for a voiding of the marriage on grounds of fraud and bigamy. You might be able to get a solicitor to write him a threatening letter to that effect. It may do the trick in getting him to agree to a Polish divorce. I'm just wondering do you think he's holding out because he wants you to pay him off? If either of you is earning good money he may think there's a cash bonus in this situation. Actually I'm sure that if you could afford it a good international private detective agency would be able to pull up a fair bit of information on his background including routing out the wife and child.