Next of Kin
You're to exterminate the entire Draconis family: mom and the four kids. The only information that Lachance can give you is about the mother, Perennia. She'll be at Applewatch, the family farm, which is just outside of Bruma. You might have already stumbled across it during the "Spies" mission of the Main Quest or during the "A Brotherhood Betrayed" side-quest in Bruma.
Perennia thinks that you're with a shopping service that she hired. So play along with her if you'd like to make your life a little easier. She'll give you all of the kids' locations, a list of presents she'd like you to buy for them, and 100 gold to cover the gifts themselves. If you're really determined to be the assassin, you can just kill her outright. The list is on her body and she's not that tough of an old bird. The dog might take offense, though. The kids can be handled in any order.
Andreas (I'll go alphabetically) is at the Drunken Dragon Inn, which is southeast of and pretty close to Atatar (you would have gone there for the Fighters Guild's "Azani Blackheart" mission). He's unarmed except for a dagger and doesn't wear armor. The only hiccup might be an Imperial Legion Trooper who seems to live in the inn's common room.
Caelia is part of the City Watch in Leyawiin. I usually just snipe her as she makes her rounds. Of course, if there are any fellow guards nearby, they take offense at that. But I'm just too impatient to wait for her to show up at the Three Sisters Inn in the mornings and go into her private room (where she can be taken out in private).
Matthias is easiest to kill in his sleep. Pick the lock on his home in the Talos Plaza district between midnight and 5 a.m.
Sibylla is usually the easiest part of the mission. Most of the time (since I'm such an avid explorer), it turns out that I've already killed her. She's a "back to nature" type and lives in a cave called Muck Valley Cavern near Cheydinhal. Well, her and her woodland critter buddies (all eight or so of them). She's kind of gone feral (as if the bearskin bikini weren't enough), so she attacks whether you're on this mission or just wandering.
Once all five of them are dead, go to Castle Skingrad and click on the well in the courtyard to get your payment and the location of your next dead drop.
A bit later on you can go back to Applewatch and find the graves of the five family members. Caelia's has a Steel Longsword that you're welcome to. If you read Perennia's headstone, a ghost will appear and attack you. But aside from that, nothing else seems to come of this mission.