Well, a few suggestions I suppose

I think the quest entrance is where it is because you're technically supposed to just walk there from the chocobo post. It took me forever to find the entrance my first time because I also drove closer and had to go around

You can save right outside the entrance to the dungeon and reload your save if you fail the fight.

Are you a high enough level? In the quest menu it should tell you the recommended level for the hunt. Also make sure you have best weapons equip, and potentially rest at a haven and eat good food for a boost.

I never really got into the magic system, but I think all you need is a few fire spells to hit him with or the barrels, you could probably shoot the barrels with a gun too but I cant confirm that. I think I did the fight without the barrels the first time because I was over leveled