Ring of Pain

If you happen to encounter an Exit Phase book at the start of the daily dungeon this achievement is pretty easy, since you can get a massive speed bonus to your score with it, I was able to get 9928 abusing that book, I didn't even kill any enemy except the ones at floor 1.

I suppose the misting vessel could also work, since you could just sneak pass every enemy.

This is not really a solution, because you cannot do a walkthrough for this achievement. There is a new dungeon every day, some are easy to finish, some are very hard. Even when finishing a dungeon I didnt get close to 9.000 points. And as you can't play older dungeons, there isnt much time to play a "good" dungeon.
Today - 24th October - is perfect for this achievement. I got it on my 3rd try (about 11.000 points without finishing the dungeon), then did the achievement with my wife's account with about 15.000 points with finishing the dungeon - at first try.
You start with a nice item which gives you health when an enemy explodes, while thanks to another item many enemies explode on death.