The Surgeon/Malus Thorm can be found in Act 2.
He can be found in the House of Healing flanked by four nurses.
I’d recommend approaching him and initiating dialogue, with speech checks you can persuade the nurses to kill each other, making this significantly easier.
To perform Surgery he needs tools, these can only be gotten from the nurses (and only if they’re alive). He’ll occasionally try to resurrect a nurse, simply focus it/them down asap.
Finish combat without him receiving a weapon from any of the nurses/performing surgery and you'll nab this achievement.
This CANNOT be gotten my using speck checks to have him kill himself.