On this page of the game guide to Borderlands 2 you will find the walkthrough description of the main mission titled Toil and Trouble. After beginning this task in the Sanctuary, the hero will have to venture to the Eridium Blight and Sawtooth Cauldron locations.
3) Bandit camp 1
4) The path
5) Bandit camp 2
6) Entrance to Smoking Guano Grotto
8) Passage to Main Street
9) Bandit camp 3
Speak with Mordecai  and use Fast Travel to get to The Dust. Drive north-west, where you will find a passage to Eridium Blight. Head south-east to the bridge . As you reach it, the further road will be cut off. Head north-east, to the passage to Sawtooth Cauldron.
Fight your way through the first Bandit camp  and go down the path marked as , to the camp in the lower part of the map . Here you should find an entrance from the above screenshot, leading to Smoking Guano Grotto .
Head inside and turn right to reach the elevator . Use the button on one of the walls beside the elevator and you will be attacked by a group of Bandits. Fight them off, killing four Ambush Commanders.
Head to the passage marked as . As you get outside, go to the camp marked with . Fight your way through Bandits and eventually you should reach a bridge  which you need to cross to the other side. Destroy the stationary turrets placed on the roofs of the buildings. Use the lever  (square on the screenshot) and destroy the Boombringer. Now you will have to return to the elevator which has been blocked . You can find the shortcut marked on the map as .
As you approach the elevator, a Mortar will exit tit. Kill him and use the elevator to get onto the roof.
Upstairs, you will have to destroy five Buzzards. I'd suggest staying by the elevator entrance, under the roof and destroy the vehicles from there. That way you will avoid being hit. If none flies nearby you, head outside for a while to provoke an attack.
With all the Buzzards destroyed, place the transmitters on the four crates. Wait for them to be taken by Brick's men and jump down (eastern part of the construction) for a shortcut to the Fast Travel. Move to Eridium Blight and return to the previously blocked bridge . Cross it to Arid Nexus. There, turn left and Use the button to finish the mission.