This video shows how to assassinate Tamir by popping out of a haystack and then immediately hiding back in the same haystack.
This mission is not difficult, but it is probably more complicated than you'd think. Start by killing the guard that stands by the haystack. He will patrol around the souk on occasion, so wait a bit if you don't see him at his station. You need to kill this guard to ensure that he doesn't witness you jumping out of the haystack and assassinating Tamir. Killing him, however, brings a minor complication. His dead body will attract the attention of passing guards, which will make it more difficult to assassinate Tamir quietly. You can get rid of the dead body by leaving the area, so that the game stops modeling it. When you return, the dead body will be gone.
Tamir will circle around the souk to insult his merchants. During his travel, he will pass the haystack. It may seem that you would simply need to jump out at the right time to assassinate Tamir, but it's a little more complicated. If you jump over the *side* of the haystack, you will mostly likely bump into Tamir or land too far away to immediately assassinate him. The trick is to go over the *corner* of the haystack instead. This puts you at just the right distance from Tamir for a low profile hidden blade assassination. However, if you see a guard walking nearby, he'll spoil your stealth if you jump out. Just remain in the haystack instead. Tamir will go around around the souk again, and you will have another chance when he comes around.
When you kill Tamir, the camera angle will change. Memorize the new camera angle - when you return from the blue memory corridor, you will need to orient yourself quickly so that you can head straight for the haystack. Chances are, the game will pause just as you are climbing in the haystack... ironically, to instruct you to become Anonymous. (The game does not pause at all if you get in the haystack fast enough.) Wait for any guards to pass before getting out and heading back to the Bureau.
That's so awsome that you found a way to do a haystack assassination in AC1. I gotta try this myself.