I can't remember how I did the first time. I probably fucked up at some point and just massacred everyone. I've played through all the missions more times than I can count, but if I'd do the mission now I'd:
1. Follow that South African guy (his name was Schmidt or something so I just assumed...) to his room, kill him, steal his stuff, dump body
2. Bring suitcase to Sheik. Wait for his messenger boy to run upstairs and check the hardware. The other guy calls Sheik who then gets up and goes into a back alley.
3. Toss coin to distract body guard watching back alley, push Sheik down stairs
4. Go to 7th floor (or whatever it was), pull fire alarm, kill that other guy, steal diamonds
5. GTFO with own suit and diamonds
2 kills, 1 accident
(To get SA-rating you could throw Schmidt's and that other guy's bodies off their balconies making it look like accidents, unless you time it wrong and some douchebag bell boy sees you)