Important: This was recorded on New Game+ with all tools and skills unlocked. Normally the only tools you can have at this point are knives and torches. The Assassin Focus ability (which you normally don't get until later) also stays unlocked.
Early Assassination
The target is behind a door until you reach a checkpoint. Previously I tried various ways to damage him beforehand and failed. For this I used the noisemaker tool modified for fire damage in a small area. First use the noisemaker to lure him close to the door, then use another one to set him on fire. After two successful burnings the target retreats farther into the room and cannot be lured anymore.
Now start the next checkpoint. The target will teleport outside the room in an injured state and two checkpoint markers above his head. Getting close to him starts the assassination scene.
Sniper
The farthest I've been able to knife Al Ghul. I had unlocked the throwing knife for far range throwing. From a far distance the game spawns a low poly NPC of the target that looks like a guard and cannot be hit with knives. After getting closer, Basim delivers a line of dialogue and you can finally knife him.
Note: Stabguy made some observations about what can delay Al Ghul spawning outside the room in the description for his video
Blitz Assassination: Al-Ghul.
The target is now in an injured state and you'll have to get close to start to start the scene. An observation I made is the target will not take any more damage although you still have the option to perform a stealth attack. The farthest knife throw I've been able to get without using lures is 98 meters.
Human Bait
This utilizes a way of getting Al Ghul off the balcony. Parry him to move him closer to the railing next to the wall, then use the kick ability to knock him off. Kicking does deal some damage, so you don't want to do that too much or he won't survive the fall.
One quirk about Mirage is the caged chickens, who become hostile upon being freed. Break the cages either by attacking them or with a throwing knife. Since Basim was closest they went after him until losing sight, then turned their hostility on Al Ghul.
Simultaneous Deaths
Basim and Al Ghul die together. I use a lift while the target deals the final blow to my health. The following scene brings Basim to life although you still get desynchronized. The last checkpoint is before the assassination.
Non Story Assassination
During the mission the game still recognizes Roshan as ally who fights Basim's opponents. I lead the target to her for an assisted kill to see what would happen. The following scene does not start (I'm guessing you are too far away from the scene area for it to properly load). After a while going through a blank screen the game goes back to normal, except Basim cannot move. Restarting from the last checkpoint puts you where you were right before the blank screen. You cannot progress on this save.
Friendly Fire Bloopers
Two cases where another enemy causes Al Ghul's death. First is when I'm trying to get him off the balcony and a guard hits him with a knife trying to get me. Second is a melee attack on ground level while I was practicing for a simultaneous kill. I had pre assassinated guards in the area to prevent things from going wrong, but was I was unaware of is the game spawns two captains in the last checkpoint before the kill. They spawn in one of the two rooms by where the target is located, whichever room is farther away from Basim at the time they spawn.
When the video said Human Bait I was thinking, "Where are you going to find a bear in the desert? Ha ha, chickens! Of course." Nicely done.