For this quest you have to kill two people; Alain Dufont and Nilsine Shatter-Shield who is optional.
Killing Alain Dufont
Alain Dufont is the bandit leader at Raldbthar. There are only a few enemies, none of which pose a challenge.
Killing Nilsine Shatter-Shield
The optional kill is the harder kill because Nilsine Shatter-Shield is walking around Windhel. I followed Nilsine Shatter-Shield around until I was hidden. Be sure to use a bow and arrow to kill Nilsine Shatter-Shield because if you use a sword in the brief moment between your attack and her death she notices you and you get a bounty.
Return to Astrid at the Dark Brotherhood Sanctuary to finish the quest off.
Full Walk Through YouTube Video