A Savior kill is when you kill an opposing player who is engaged in combat with someone on your team. Kill them before your teammate is killed, and you'll earn a savior kill (and a nifty 300 XP Bonus!). You'll know you earned one when it pops up in big letters under your kill score at the top of the screen. This popped in my second game online.
THE KILLS MUST BE DONE WITH THE SAME CLASS E.G. ALL 5 WITH RIFLEMAN OR ALL 5 WITH ENGINEER*
Perform this five times and this achievement is yours. If there is something wrong with the solution, please do not hesitate to contact me.
*Thanks to Grimdog John