It is not fair or helpful to ask this with so little context! It is a very unusual phrase. Acknowledged = recognised/accepted/'taken as read'. Ability = skill / capability. Dental is used here strangely. It is normally related to teeth - particularly fixing teeth, as dentists do. But here - it refers to oral skil l- in particular - the ability to speak.

I agree there is too little context to be certain what the phrase means. However, based on what we do have, I think the phrase "a domestic cat of acknowledged dental ability" refers to the fact that people recognize that the cat is able to bite very effectively. То есть, все признают, что кот/кошка кусается.