You want to get outside into the courtyard. I'm not sure exactly where you are, but if you are where I think you are, you should come across a hallway before going upstairs. You should find an exit there that leads you directly to the courtyard, avoiding the need to go upstairs.
Once outside, you need to get to the garden (just follow the wall of the courtyard: watch out for guards) and the solarium.
Once inside, you'll hear Rulindil talking to his subordinate. Once he leaves, head to the room to the right of where Rulindil enters (again, watch out for guards). Here, ransack the room and look for dossiers found inside of a chest. You'll also find a interrogation chamber key.
Once you have that, you need to escape. To do that, head down into the dungeon, once more dealing with the guards that you find there. You'll find a prisoner locked up as well as a chest that contains another dossier.
Finally, you'll need to speak to and release the prisoner: Etienne Rarnis. Once freed, you'll be rushed by even more guards. They'll have the trap door key, which you can then use to escape the embassy directly from the dungeons.
When you drop through the trap door, you'll enter a cave where you'll have to fight a troll.
After that, you're home free.
Best Answer
I haven't been doing to blades questline, but I guess it's as simple as just reloading the save when you walk into the sleeping giant inn and not talking to her. If you talked to her and then did other unrelated stuff, find the last save before entering the embassy