This quest is actually very easy. First you talk to Nazir who tells you to go to Whiterun to confirm with Amaund Motierre that the assassination is still a deal. Afterwards you go to the Katariah which is laying under Solitude in the ocean.
On Board the Katariah
On Board the Katariah you encounter many of Penitus Oculatus Agents. Your best bet is to use stealth and a bow and arrow as you can catch many guards by suprise or even kill them before they discover you. I found that this made this quest very easy and I didn’t even come close to dying once. Eventually you find yourself on the deck of the Katariah. There are about 4 Pernitus Oculats Agents on deck. Kill them with stealth. Next you go to the Emperors quarters where you find Emperor Titus Mede II sitting behind his desk defenseless.
After you have done the deed report back to Nazir in the Dawnstar Sanctuary.
After you have gone back to Astrid at the Dark Brotherhood Sanctuary she will ask you to kill Vittoria Vici at her wedding in Solitude to cause confusion. This will seem hard but it isn’t very hard at all. Find your way up to the top of the walls near the wedding celebration. If you are having trouble look at the video I linked at the end of this paragraph. Don’t bother with sneaking because to get a shot on Vittoria Vici you won’t be hidden. You get extra money if you shoot her whilst she is on the balcony above were she normally sits. I found the best way to get her up there is to wait for an hour again and again until she starts walking up. I used a bow and arrow to kill her. Afterwards be sure to run towards the quest marker as fast as possible. Once you are inside the guards in Solitude will stop looking for yo and you won’t get a bounty.
After you have joined the Dark Brotherhood and completed With Friends Like These… you have to talk to Nazir about contract work. He will ask you to kill 3 different people around Skyrim. Only one of the three is somewhat difficult because it is in a built up area.
How To Kill with Stealth
Even if you are hidden you cannot use a sword to assassinate someone, nor can you use magic. In the brief seconds before their death they will notice you and you get a bounty. The only way you can perform a stealthy kill is through using a bow and arrow. I decided to use a deadric bow which you can make with one deadra hearth and 4 ebony ingots, if you want to upgrade it too. A guide to deadric armor and weapons is here.
If you haven’t done the Dawnstar museum quest speak the to guy outside the house next to Beitild’s house and he will go inside. Then you can lock pick Beitild’s house and get inside without being noticed. Beitild is only home during the night when she sleeps. I found here there around 2 am. Use a bow and arrow to kill her in bed whilst hidden, otherwise a guard will come into the house and attempt to arrest you.
Narfi is very easy to kill. It doesn’t matter when you kill him as long as you are hidden. Nobody is near where he lives, so you won’t get a bounty for killing him. I found him standing around near his hut during daytime.
Killing Ennodius Papius
Just like Narfi this guy is very easy to assassinate. I found it best to kill him at night when he is sleeping in his tent. Be sure to check that you are hidden and shoot him from a safe distance.
After you have killed any one or all of them you can return to Nazir and collect your bounty. The Dark Brotherhood Quests will only advance after you have killed all three targets.
To start this quest you need to go to an inn and ask the innkeeper if he/she has heard any rumors lately. They will tell you about the Shrine of Azura which will start the Black Star quest and give you a quest marker to the shrine. You can find the shrine south-south-est of Winterhold on top of a mountain:
She will ask you to find the mage that knows something about the Black Star. He is located in the inn at Winterhold. You can talk to the innkeeper and you will get a quest marker for the location of Nelacar. For me he was in one of the side rooms of the inn at Winterhold.
This former tower is full of mages. The main problem that mages poses is getting close to them. Once you can use your sword or any other close combat weapon on them they will die very quickly.
The best way to take out mages is to use bow and arrow. Be sure to be sneaking because often times you can one-shot mages with a good bow and some decent arrows.
Snealing is also very powerful when using a sword or similar close combat weapon. I usually like to use the Wabbajack on stronger enemies because it has a chance to instant kill them or turn them into a chicken or rabbit for a while which will let you get close to them easily. You can find a full guide to getting the Wabbajack here.
Inside the Black Star
After you have collected the black star at Ilinalta’s Deep you have a choice. Either you can bring it back to the shrine were you will receive a soul gem that traps non-human souls or you can go back to Nelacar from whom you will receive a star that traps human souls. That is what I went with because a human soul is always the best soul possible.
To get the soul gem you will have to enter it. Inside you meet 3 Demora Markynazs and Malyn Varen. You can use the same strategy I outlined earlier to defeat these enemies. Remember the loot the Demora Markynazs because they have deadra hearths on them