I found with moderate anarchy and a Jill of All Trades Mod Torgue Spitter ARs were very effective so I would be willing to bet the Ogre is really nasty with her.
The Fibber with the barrel that makes the shots bounce and split is overpowered as the natrual ricochet of the weapon means that shots that fly towards the target due to close enough get no damage reduction.
The Sham with a variety of launchers (especially Topneaa) works really well as well since high anarchy makes the shots very deadly and the Sham can absorb the splash to save you from shots that hit you due to poor accuracy.
Look out for Texas prefixed Jakobs Shotguns with a mag sizes equal to or less than the ammo consumed per shot +1. With the right parts they can have a 1.9s reload and the mag size means you get 1 shot before reloading and can hold the trigger in combat for fast anarchy building.
Playing: Borderlands 2, Final Fantasy XIV Beta and Terraria