Can I disclose a conflict of interest with some professors from a particular university in responding to comments? I have been given comments for a major revision from a respected journal. But suddenly, I guessed with a high probability that a person who is a long time adversary of my supervisor may be behind this comments and he won't be satisfied no matter what I do. 

What should I do? Can I disclose a conflict of interest with one or two professors from a particular university not to be a referee? What may happen?
I'd advise against such a move, which can be seen as a way to avoid a complex revision. 

Usually, at the time of submission, journals allow the authors to specify non-preferred potential reviewers, either directly through the submission management system or through the cover letter. If you think that someone can be strongly biased against your work due to a conflict of interest, that's the time to voice your concern, not after the review.