I found that there seems to be a bit more 'swim' to Snake's aim on Extreme. Or some inherent inaccuracy to the Mk 2 at a certain range. Sometimes you can see the tranq dart's path differ from where the laser sight is pointing. Just the tiniest amount, but sometimes enough to put a dart into the wall behind someone's head instead of where you wanted it. I could be imagining that, though.
Well, sure enough I tried again and got through it on the first try, as well as the next two sections. This game knows the exact moment I start getting overconfident and it never fails to punish me for it. Here comes dat bike chase, woo!
That is definitely the case (although whether it is exclusive to Extreme or not I'm unsure) which is why it is can (for Act 3 anyway) help to aim at where the enemies mouth would be, so that the laser sight is on the enemies head, a significant portion of it is covering their chest and most of the remaining area is occupied by their head, leaving only a small room for error compared to just aiming solely at their head (where, although you'll make the shot correctly most times, as you've said, the sway can affect some).
However, you've finished it so that's pretty irrelevant now! Well done on managing to get through it despite the frustration. Although, I would take a break if you're frustrated now, the bike chase will bring a new meaning to the term when in the context of Metal Gear Solid 4
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First trophy run complete, earned the Solar Gun and ended with the rank of Octopus (other emblems awarded being Scorpion, Inch Worm, and Hyena), marking the first time I've ever finished any MGS with no alerts. Will consider trying a Chicken run next.
No Flashback Mania trophy for me just yet.
Well done on getting through the game with no alerts! If you're going for the trophies I'd actually advise you get the Big Boss Emblem next provided you:
Have the Anti-Material Sniper
Have 2 Chaff Grenades minimum
Have 50 tranquiliser bullets for each gun.
Have 50 V-Ring bullets.
The reason I'd advise going for Big Boss now as opposed to Chicken is solely because since you've finished the game with no alerts just now, you are likely to have memorised the enemy patrol routes and positions to some extent which will make it easier for you to transition to a Big Boss Emblem run than it is from Chicken to the Big Boss Emblem. Of course, it's up to you and the order really doesn't make a huge difference.