-Physical Attacks work great against this opponent, especially if you have Cid equipped with Trident in your group.
-After fighting Red Dragon, go to go to your menu screen and select "Marteria". Take all your Materia off except for All Materia, Restore, Barrier, Time, and Deathblow. If you want your summons, keep those Materia equipped. The Materia is taken off becuase your health points will go up. Keeping Restore allows you to heal your party.Make sure to have at least one All Materia equipped, and have it in a double slot with either Restore (recommended), Barrier, or Time. Keeping Barrier equipped allows you to cut off some damage that Demon Gate has sends. Keeping Time equipped will allow you to cast the spell Haste. Deathblow will either have a critical hit or a miss. Remember that Demon Gate has a high magic defense.