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.