Straight to the point, here's an image with the route and steps:
http://i.imgur.com/Y8DZ0DY.jpg
So, the biggest tip I can give you when doing this (and I'm sure it's been brought up before), is that you don't need to let the mobs kill you to reset the encounter.
We first found that running back to the safehouse for the original method (with Bullet King) would reset the mission, so we got to avoid the respawn loading screen.
After more testing on this boss encounter, we found that you just need to pass into a different territory to reset the encounter.
For those at work who can't see my image (it's just an imgur link), here's the steps I typed up:
Get to the North border of Hudson Yards, where Hell's Kitchen starts.
Run straight South down the street to where the orange circle is on the map to the left.
There is a named boss "Erksine"and 2 cronies. [Note: Don't kill both cronies and the boss, or this farm is toast]
Kill Erksine (I typically stop at the police car and snipe him twice as he runs up to me) and he will drop 2 Superior drops and some Phoenix credits. I've also had two 'Caduceus' drop while farming this (High End Weapon).
Now that you've killed him (I also wait to pick stuff up until I've done it 3-5 times, to speed the run up), run back north and make sure that you cross into Hell's Kitchen territory (the text background should turn orange to indicate that).
This resets the encounter. Rinse and Repeat to farm your Phoenix Credits and crafting materials!
Note 1: There is a bonus citizen in need, so you can build up your wardrobe too!
Note 2: I run Healing Station +Ammo Cache so I don't need to hit the safe house. Seeker Mine +Gas Charge lets you get in and out to pick up loot without worrying about taking hits from the cronies.
A couple of pros and cons vs the original route:
CONS:
This one takes longer to run, length-wise
There's only 2 other bad guys. Keep your aim on point and don't shoot the cleaners pack or you could end this encounter by accident
PROS:
This one may be available if you don't have Bullet King available (kind of a big pro is actually being able to do it).
There is only 2 other bad guys, and 2 of the 3 have axes, so you can mindlessly do this without getting shot
It's a straight line, and as mentioned, it's only 2 other guys, and 1 guy with a gun to worry about. I've been farming this while watching Netflix for a few hours. No headset needed. Minimal effort needed to "pay attention" to the game.