Dishonored

The outcome is dependant on the path you chose either loading the Low Chaos savefile from previous DLC "Knife of Dunwall", where at the end of the fight you kill Corvo, or if you choose the High Chaos savefile, where Corvo kills you.

Either way both outcomes grant you this achievement, so you don't need to worry about it.

P.S. Low Chaos doesn't grant you the kill you made during the fight, so Low Chaos run is not voided and this won't grant you the kill in the statistics at the end of Level.

Most of the playthrough will be very similar to previous stealth playthroughs. In the end it may be a bit unclear how to take out delilah non-lethally:

If you steal the painting at the end of the void level and replace it with emily's after Delilah performs her ritual and turns her back to it you will get the non-lethal ending without detection of the statues.

I don't know if this is merely coincidence but it seems that Corvo is beatable on a Low Chaos continuation of the knife of dunwall. I tried 10 times with my high chaos playthrough but after failing each time I tried once with low chaos only to beat him on the first attempt.

Keep blocking his sword and get in as much hits as possible while he is staggered.