Credit to "Amir Garis" on YouTube.
Within 10 seconds of starting a procedure, you need to grab a metal instrument and jam it into the electrical socket.
This will then invert the controls, making the surgery much more difficult. Choosing a surgery that you feel comfortable doing will help. Taking a slow and careful approach will also help, as there is no real time limit on completing the surgery.
Getting this achievement along with "Performance Enhancer?" will help greatly with getting used to the controls for "And They Said It Was Impossible!".