So some of you are probably thinking about hunting your first argopelter soon. A lot of people have different methods - Some like to build fences to confuse the argopelters, for example. I personally prefer a method with less setup involved, and that's what I'll be showing you now.
The first step in my method is to find a good place to lure the argopelters to. It should be fairly open, with trees nearby on the edges, but not too many. The idea is to make the argopelter have to run through the open area to cross form one side to the other. This gives you plenty of time to land a hit on it. Personally I use halberds, as it's easy to land on the argopelter while it moves, but it's possible to do it with a roundhouse kick or even a sword if you can get the timing more precise. Anyway, you'll find a picture of an area I like to use below.

As you can see, it has kind of a semicircle of trees, and I move from one side to the other to get the argopelter to run between them in order to switch trees. While it's heading towards me, I move out to meet it, hit it, and then move out of range of the tree it's going to climb. Be careful about how large the clearing is though: If an argopelter tries to move but doesn't find any trees near enough, it will despawn, effectively wasting any work you put in luring/killing it.
That's the general idea, it's pretty easy to kill them with this method, just takes patience. You can hunt them from pretty low biles, I'd recommend 40-50 to start with, just to avoid you getting screwed over by some high rolls if you get caught by a branch or two. Remember argopelters deal highly variable damage so try not to risk taking any hits. My last tip is to make sure you conserve your phlegm. You don't need to always be running, so make sure you toggle it on/off as needed to avoid running out of phlegm.
I apologize in advance if this guide has any problems, it's my first time writing one, and this was written at 5 AM, which is probably not the best idea I've ever had. Please let me know if you see any mistakes so I can correct them.