Some definitions from Cambridge dictionary:
Perform: to do an action or piece of work.
Accomplish: to finish something successfully or to achieve something.
Realise: to understand a situation, sometimes suddenly.
The doctor performed the emergency surgery under very adverse conditions.
The doctor accomplished the emergency surgery under very adverse conditions.
'Performed' is the most likely answer as this is the word used to describe the act of carrying out surgery.
'Accomplished' is less likely to be used within this context, but not impossible. The meaning would be slightly different, indicating more than just the carrying out of the surgery, but also indicating how well the surgery was performed.
I hope that helps.