It seems pretty much impossible if you try to give him a fair fight; that is, dodging, dashing, studying patterns, and so on. He's way too fast and does way too much damage for stats and abilities to matter all that much; the only thing that counts is sustained damage while he eats your dust. So, skyrail. And then the only difficulty is preventing him from despawning, which he's finicky about. In the end all I had to do was watch his icon on the minimap, make sure he wasn't falling too far behind, while keeping my speed around 80 mph. After that, point in the other direction and hold down left-click.
(Nebula armor is obviously useless under such circumstances, so I went back to Spectre.)
Has anyone done it some other way? Did I miss something? Is there some combination of buffs, armor, and accessories that let you fight the Overseer fairly, like a traditional boss?
I didn't want to cheese him, but honestly, when something does 400 damage to me twice in under a second, I'm not sure how many options I have.