The Introductory Session - Grandmaster Style
Here's the introductory session, done Grandmaster style. I set out to gain the highest amount of points in those three kills.
The first trick is that you will use the profile set you used last in the session. This means that if I play with my defensive set in a game and then select the introductory session, I will play the introductory session with the defensive set as well. You can't quit the game, or go to the main menu, though, otherwise it will select your first profile set (default name PROFILE SET 1). The profile set I used:
Ability 1: LL Poison* (maximizing score)
Ability 2: LL Smoke (normal smoke, strong smoke or RR smoke can also be used)*
Perk 1: Silent hunt (not really necessary)
Perk 2: Boost cooldowns (not necessary, but handy to have)
Loss streak: Score 2x (not applicable since you can neither die nor get your contract stolen)
Kill streak: Score+300 (3 silent kill streak, since you only get to make 3 kills)
The session always starts of ridiculously. When the game is going in slow-motion, you can't do anything at all. While I'm bashing A to continue, the priest gets way ahead of me. It's really annoying, during the first kill as well. As the guy gets in sight, as your compass turns full circle and as the 'kill'-button appears above the targets head, the game goes in slow-motion. Luckily, I was in a group, so I could keep moving with my target. I already was fairly sure it was the barber in the back of the group (simple rule: it's never the one in the front), but after I turned the camera to lock on him, the kill-button appeared and the game went slow-motion, so I was absolutely sure it was him. A simple focus-hidden-poison kill gets me to a good start of 1050 points.
The second kill is more elaborate and took some figuring out. If you near your target on the ground, he will run away once you get within a 10m radius of him, even if you're in a blend group. This makes it very difficult to get him without a chase. If you have silent hunt on, you can get a discreet kill, but I was going for maximum points. I figured out that he would only run away if you're both in his line of sight and on his elevation level. If you're in his line of sight and climb down to his elevation level, he will run, so I use an offensive smoke bomb to prevent that. Dropping down the last part removes my incognito, but that's good, since the kill will deliver 1150 points instead of 1050 points, because even though you miss 100 points by going from incognito to silent, you get 200 points for variety.
The last kill is a free 1050 point kill, since the target will stand in blend groups most of the time. Topping those three kills of with a streak bonus of 300 points leaves me with 3550 points.
Since the second target is so damn annoying to kill, I challenged myself to get 3 incognito-focus-hidden-poison kills (aerial acrobatics would've been to easy). To do this, you have to make sure the target is near a place where you can screen him (you can scare him away by just walking up to him). The ideal spot for this is under the Pantheon, since there are so many pillars. You hide behind the screen, so the line of sight is broken, and then quickly pop out and throw a smoke to prevent him from running.
I also show off how stupid the whole elevation-level thing is. I'm right in front of him, yet he doesn't run away. The weird thing about this clip is also that he didn't attempt to run away after I poisoned him.
*LL means long lasting, RR means rapid reload.
You could get more points on a kill with your loss streak. Just kill enough random civilians, get the 2x, and do whichever one of these methods got you the least amount of points. Altogether, it's a good push in points. Nice idea using the intro session like this.
As I remember it, killing civilians does not add to your loss streak, otherwise I could've doubled the total points.
What? It does for me. O_o
I'll figure out the mechanism soon. 
Maybe it doesn't work in the Introductory Session only?
Or I've lost my ability to count.
You need to start a chase first. Then just lose the chase or kill a NPC.
There we go, that's the solution. Thanks Pavan!
Thanks, Pavan! I never start chases, so, yeah.
Thinking about it, starting chases is not very grandmasterly, is it? Or killing civilians, for that matter.
I think as long as something is used for a strategic purpose to gain a big advantage, it's still grandmastery. The Barber would just keep wondering why you're failing so much, then BAM! Tons of points out of nowhere.
haha, I'll get on to it then.
May have the new video up tomorrow.
Wait, use the 2x loss streak on your first kill, then you still get the kill streak bonus after the final kill, giving a better amount of points than I originally thought. Aww yeah.
Thinking about it, starting chases is not very grandmasterly, is it? Or killing civilians, for that matter.
You'll have to change the name to Grandbastard Style.
I took the whole challenge as solely gaining the most points possible in the Intro Session. I didn't know you had to have morals to do it.
You get to hold your killstreak within the loss streaks, actually. It surprised me. The maximum score then becomes 7100 points.
Yay for exploits! 
That is only 250 lower than my max session score. And higher than most of my friends' max session scores. Maybe I'll do this on their accounts and see if it affects the stats.
The max I did last night in this was about 3900. I hate going through the slo-motion pauses, so I only did it once.
It's fairly easy to get max score, actually. Using LL smoke, you can get easy hidden-focus-poison kills on targets walking past blend groups. That's usually the way I get it on the first target. I got lucky in the vid. 
I tried my idea of using the loss streak, but I guess it didn't work? I'm too lazy to do the math. Haha
The loss streak definitely works. I tried it out yesterday. Now only to record it (didn't feel like it yesterday night, I was happy enough playing with other people ).
We should get at least 1 person to record THB matches. Multiple views between us would be fun to watch. Just a random idea.
Anyways, I don't know why I got such little points when I did it. I probably did something different from your strategy somehow. I only watched it when it was first up, so maybe that's it.
The first kill should yield 1050 points (2100 points with loss streak). Usually, the best route to take is through the Pantheon. Be sure not to perform any high-profile action whatsoever in front of your target, because you will lose your incognito. In the vid I use silent hunt so a small screwup (one step in line of sight) doesn't blow the whole run.
For the second kill, I use an ordinary roof strategy (ordinary is actually a pejorative term in Dutch ), only dropping down the last bit, and dropping LL smoke before I do. I also make sure the target is in a blend group (scaring him away once will make him go to one). This allows for a focus poison hidden kill, with variety, which adds up to 1150 points (2300 points with loss streak).
The third kill is the easiest. Just walk up to the guy standing in a blend group (if he's not in a blend group, he'll get in one soon), blend, focus and poison. If you can't get that last one, your game's broken or something.
Without loss streak, you got 1950 points. I assume you got the last kill right, so that leaves 900 points. 100 of those might have been a chase kill because of the running target. Leaves 800, which is the same as a silent-hidden-poison kill, without focus.
Did you get your killstreak?
...okay, I did all of that exactly, except the second kill, I got silent for variety. I guess I would've gotten it anyways. Most likely that's the problem.
Joey, I don't know what you did, but it's weird. If you got 3900 points, that means the difference with the maximum score is 3200, which is the same as 1050+1150+1050. O.o
I don't know! It's confusing me! I'll just try again.
You do that.
I take it you never saw my video on multiplayer...
In a live match I managed to get 2900 points by using 2x loss streak and 5 kill streak at the same time, also with poison. If I really tried, I could have gotten extreme variety, so thats another 1200 points.