Sacrifice five to kill
This is the technique in its abstract form. It involves a capturing race in which the attacker willingly sacrifices 5 stones ...
... to next kill with a throw in and a play at the vital point. Incidentally, the throw-in is better style than playing immediately, for reasons of ko threats and ko value.
The crux is to create potential for throw-in, and not, as here, allow White to capture four stones solidly, after which she is alive.
This technique is mentioned in the hard section of gogameguru's problem set week 14: http://gogameguru.com/weekly-go-problems-week-14/.