Ghostrunner

The best levels to do deathless would be A look inside and In her own image (Hel fight).
As for why this is the case, it’s relatively simple for both:

• A look inside only has 2 combat encounters - one of which can be partially skipped with little issue - in the whole level. I would recommend doing this one on Hardcore Mode if you’re pretty confident in your abilities, as the Cybervoid segment - and all others that follow after this level - is skipped in Hardcore Mode.
• The fight with Hel herself has no checkpoints, so the only thing that’d be tacked on to get this achievement would be the Cybervoid segment where you’re introduced to Surge and the simple task of getting to the elevator.

As a side note to end this off, this achievement can’t be earned in the Classic variant of Echoes as the teleport in the Cybervoid segment is counted as a death.

You can cheese this one and couple it with the achievement for killing 23 enemies in a row without dying. Cheesing this means it's the LONG method of using your abilities on every enemy and waiting in cover for your abilities to regenerate to use on the next enemy. With my load out it seems like it regenerates about every 3 1/2 mins. This will be slow, but it's also safe. And this game is very unforgiving

Now if you want to speed the regeneration up you can use abilities that will regenerate faster on kills or whatever. But it's suggested that you play through the game until you have all the abilities unlocked so you can have a good feeling for which ones is best. Choose whichever one you want to use. The best would probably be a mixture of Tempest and Overlord. Tempest would be good since it has long range and has a wide area of effect. But you will want to switch between the two because you will have instances where you will have 1 enemy and no way to kill them off with overlord and you would want to use tempest at that point. You may find blink helpful to pick some off quick at the end when you dont want to stay out in the open very long.

Another thing that using Overlord can do for you is that if you have an enemy that is tricky for you, even of he is alone, hit him with overlord and he won't attack you leaving him open for an easy kill until overlord wears off.

You an also equip upgrades to get a wider/longer area of effect. Also if you equip the cross looking icon, "Focus: Overclock" you can regenerate your abilities MUCH faster than the 3 1/2 mins.

With all of that being said, I DID find it easier for ME to just play the first level normally without cheesing it. I just made sure to make use of aerial maneuvers where I could hold the dash button down to go into slow-mo and only dash at an enemy after I could dodge their bullet. But there's nothing stopping you from cheesing this and rushing enemies with blink and so on and waiting for them to regain before moving on to the next enemy.