You can get this mission by talking to Sir Hammerlock in Sanctuary after the mission "Bright Lights, Flying City". Talk to him and he will tell you of the monstrosity that took his various limbs. He will then give you his arm in the hopes of using it to lure the creature out of hiring to kill it.
- XP: 3859
- Money: N/A
- Gear: Shotgun
Head to the Highlands - Outwash area and visit the Extraction Plant. At the beginning of the plant, you'll find a large body of water on the right side. Make your way over there and stick Sir Hammerlock's arm on one of the pillars. After a few moments Old Slappy will appear.
Old Slappy is a very large Thresher but he also uses his tentacles in some intersting ways. While he still uses his tentacles to attack you like other threshers, he'll also hold them up in front of him so that you have trouble attacking him. You can shoot the tentacles in half so they will leave you alone but they will eventually return. The upshot of these tentacles is that you can shoot one in half for a second wind if you need it.
Despite the difference, how you fight this Thresher isn't particularly different from how you fought the Gluttonous Thresher. Whenever he burrows underground or he is attacking you with his tentacles, sprint away but when he first errupts, shoot at him. If you can keep doing this, he should come down in no time. Just be careful and be particularly vigilant about running because his tentacles can deal some serious damage.
After you've taken him out, collect all the Eridium he drops, grab Hammerlock's arm and return to him in Sanctuary for your reward.