Beitild lives in the city of Dawnstar and has a house there. You can use this to your advantage and wait until night when she’s in her house asleep. There IS a lock on the door, but it’s a NOVICE lock for pete’s sake! If you can’t be bothered waiting, you can just run up to her and pummel her to death (and then kill all witnesses to remove the bounty from your head). It’s your call.
Anyways; once you are inside you can kill her with little trouble. Be sure to loot her once you’re done. Now you can either do the next TWO assassination or you can report to Nazir (I suggest doing the next two; be sure to save!). This contract is worth 500 Gold.