Gilgamesh I never had a problem with, and there's no official strategy for him, just level up. And from what I understand,the emulator is much harder.
As for Omega and Shinryu unless your around 70, dont even try. The ultimate weapons barely scratch them, they counter magic, and have superb attack and defense.
Think I did it by hoaring dragoons jump for a long,long time.
www.gamefaqs.com probably has a solution.