Head on through the landing. There is an Ammo Dump Vending Machine waiting here for you. Restock on what you need then search the Eastern side of the landing you are on. There is a lever that will digistruct a loot chest for you.
Jump to the area below. This is Butcher Base where the next part of this mission is.
When you land you will need to fight on through 4 Horned Skags then you will encounter Dukino's Mom. The tactics remain the same, as do the attacks. Go for the mouth when she is charging her orb or firing the laser. It will not be too long before you claim victory here.