I stumbled on this solution for the original Xbox 360 version:Solution for Enough Coin to Disappear in Dishonored
It suggested that low chaos is not necessary. You could complete Witches of Brigmore in high chaos and as long as you finish with 10000+ coins you will still get this achievement.
I can certainly confirm that this worked for me on the Xbox One Definitive Edition. I killed just about every enemy, I got the high chaos ending, and the achievement popped.
At the start of the DLC I imported my low chaos save from The Knife of Dunwall because I finished it with just over 4000 coins.
Necrolampoon has confirmed that you can still get the achievement by beginning the DLC without importing a profile from KoD (in which case you begin with 3000 coins) and still killing everyone you see. JJ Nerdstrong has confirmed that if you start with a new game in this DLC, and DO NOT import a previous save, then when you collect your gear from the chest at the start you will be given 3000 coins.
From what I have read elsewhere there is about 7700 in the entire DLC. So as long as you explore almost every area you'll get over 10000 even without importing, but obviously having more to start with does make it slightly easier and reduces the margin for missing out.
BaldyGamer has also confirmed that you can earn the achievement by loading a high chaos save from KoD and finishing in high chaos.
For me this achievement popped along with the high chaos ending achievement (All Come To Ruin) during the credits.