An easy way to get this achievement after you have completed the DLC:
1. If you have Mayhem Mode on, deactivate it on Sanctuary.
2. Load into Negul Neshai map.
3. Rush through the map to the boss fight with Empowered Grawn. (Deathtrap will always respawn here to aid you in the fight, even after completing the DLC).
4. As soon as you drop down into the arena turn immediately right and then go up the first small flight of stairs before turning immediately left and continuing up the stairs into the sort of “control room” at the top. This has a large circular power unit of some kind (not sure how best to describe this, but you can’t miss it) right in the middle of the far wall.
5. Jump up onto the desk to the right of this unit and tuck yourself into the gap behind it. You will now be completely unreachable by any enemies and take no damage during the boss fight, which, if left alone, Deathtrap will eventually complete for you.
6. Leave the game alone until Deathtrap kills all enemies, including the Empowered Grawn, which given time he will definitely do on his own.
7. Quit out, load in and repeat the above until the achievement unlocks.
I’m not sure how many kills Deathtrap made on my first full run-through the DLC, but I did that on Mayhem 4, so it probably wasn’t many.
Switching to no-mayhem and doing the above: it took me about 3-4 reloads and a little over an hour to get the achievement. Along the way I also got a nice anointed Old Guard shield to drop without me killing a single enemy (and with no mayhem mode on). Deathtrap did all the work…
Hope that helps. I’ve tried to explain as best I can so please don’t down vote me if it doesn’t work: it 100% did for me, so the only other reason it won’t for you is because I haven’t explained something properly… happy to try to add to the above if I have missed something…
UPDATE: Thanks to KainMarks for informing me this doesn't work with FL4K unfortunately as he's too big to hide in that spot. I did this on Moze so I can't see why it wouldn't work with Zane and Amara as well: but not FL4K it seems...