You can go left, since Dom takes the ladder behind you and goes right. When you see Alpha 7 drop, turn around an go up to see another grinder drop. Keep following this path and you'll hear and see that Carmine is under attack. Run to the vines and cut through them, then take cover and use your Lancer, Boltok, and frags to clear out the enemies.
When they are gone, feel free to swap out your shotgun for a Hammershot and get all the ammo, then go pick up the Lancer by the lift and ammo box as it has full ammo, but DO NOT pick up the ammo box just yet.
Next comes a big fight with a ton of Drones and a few Tickers. I used the Hammershot to take out enemies to the left, then switched to the Lancer when the Tickers showed up.
After the fight, use the ammo box to refill, then send the lift on its way. Follow it and then head down the ramp to the fight; and there are items by most of the lifts. When you reach the sandbag barriers, take cover and start shooting. There are two ammo boxes behind you if you need them, otherwise save them. You should use the Lancer here as Tickers do show up. After you kill a bunch of Drones, Boomers down the dark tunnel will approach, but take out the closer enemies first. Pour rounds into the Boomers and the fight is over.
Collect ammo knowing that you're going to trade your hammershot for the Boomshot they dropped. This is basically a grenade launcher. Lead your botany club down the dark tunnel as that robot only now reveals he has a flashlight on him. You finally meet the Wretches that charge down the narrow path. Pour lead into them and be aware the some may climb up from the sides, which makes good use of your chainsaw. Slay them and proceed through the vines.