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The key is to save every time you achieve something significant.
I thought Mission 3 was very hard - assassinating the two generals in the park - that one took me a fair few goes to complete.
I've finished the game twice over, so if you get stuck again, just ask and I'll tell you what I did (if I can remember). There's several different ways of completing most missions.
Go into the main room where the piano is and hang about - keeping an eye on the Russian secret agent.
When he escorts the ambassador out of the room, follow them (carefully).
When they are in the room with the safe, kill them both, take the key from the ambassador and open the safe - get the briefcase.
Store the briefcase somewhere.
Then kill the general whilst he's in the room he keeps going to.
Go back and get the briefcase.
Walk out of the party.
This is how I did it, although I had a little difficulty getting out of the building with the briefcase.