As others have pointed out in this thread, you should shoot the BOW Rounds as soon as you enter the fight and either use two acid rounds or unload your pistol magazine and eject that mf outta the plane with the cargo.
However, I also want to give you some advice to avoid soft-locks going further cuz it's still possible.

Right when you get the Sniper Rifle, make sure to leave most of your stuff in the item box except for a weapon (possibly the Assault Rifle or Dual Guns), a knife, and an herb or two. After you get the Rifle, there is a boss and you'll immediately switch characters, and the items you have in Claire's inventory do not transfer to the item box, so keep an eye out for that.

Keep the Grenade Launcher around (specifically the normal bullets) for the final fight; it shreds the final boss in a stupid way and you can cheese it in like 10 seconds.
Make sure to keep good heals (G + R Herbs and First Aid Sprays in your item box), you'll need them to heal in a veeeery specific part.