An annullment? I certainly hope the Church turns him down if he tries for one.
Unless something has changed in the past few years, Gibson--like his father--belongs to a splinter sect that teaches that the current and recent Popes in Rome are usurpers and heretics. The sect does not recognize the authority of what the rest of us would call the Roman Catholic Church.
So I don't know what Gibson's denomination's rules are on annulment, nor to whom he would have to appeal for one.