I can't get this either (GOG version). I tried :
  • Killing him and the nurses while surprised in one turn
  • Killing him on turn one after nurses practiced on themselves
  • Convincing him to kill himself.
I was able to obtain the soldier inspiration rewards which seems similar:
  • An Apple a Day Keeps the Scalpel Away: Defeat the Surgeon without being operated upon.
  • Masterful Execution: Kill any of the bosses in and around the Shadow-Cursed Lands in a single round of combat.
But the achievement itself won't pop up no matter what.