The Gluttonous Thresher is a large Thresher with an appetite for metalic objects. The Thresher is likely the source of many missing Loaders from the nearby Hyperion Extraction Plant. This will likely be the first Thresher you encounter during the mission "Bright Lights, Flying City" in the Orbital Receiving and Processing area of the Highlands - Outwash.
This is a rather tough battle so you may die a bit before you get this. First, this Thresher can regenerate shields. They don't seem to regenerate like normal shields so they may appear to spontaneously recharge sometimes. Aside from that, the Thresher also has a lot of health, can tunnel under the ground to close in on you, swipe you with it's tentacles if you get close or burrow the tentacles under the ground to hit you behind cover. On top of that, different types of Loaders will enter the area to attack you as well.
While the Loaders might seem like a little bit much considering the strength of the Thresher, you should consider them fodder for your second wind. Try to shoot the legs off of a couple of them so they are damaged and crawling around, then engage the Thresher.
When fighting the Thresher, you want to either be sprinting or shooting. If the Thresher burrows under the ground or is hitting you in any way (behind cover, too close) then sprint away from the Thresher. As soon as he comes out of the ground, turn and start shooting at his eyes. Keep shooting until you need to reload or until you start getting attacked again. Continue this patern and use the Loaders for a Second Wind. Just watch out for all the EXP Loaders who can really interupt your flow.