Pelican riding via Shade launch
In this method you perform a Shade launch to get yourself knocked onto the top of the incoming Pelican, which you then ride down to the ground. Suitable for NTSC/PC, unsure about PAL.
When you cross the loading point in the passage just before the bridge, four Grunts spawn just outside in randomized positions. You need to do sufficient killing to end up with two dropped plasmas close to the Shade on the right. It can be problematic to obtain that situation however. Ideally you'd want the grenades to come from a single Grunt, partly because it's good to have the grenades close together, but not all Grunts carry two plasmas, and even if a Grunt does carry two, he may drop none or he may drop them in an unsuitable place, such as too close to the bridge rim. I'll talk more about engineering things later, but let's assume you end up with a situation you're happy with.
Quickly melee the Shade to get it positioned as desired for the forthcoming launch. Preferably have a plasma pistol for this because it seems to have the highest melee rate, though the AR and plasma rifle are almost as good. Speed is relevant because the Pelican is already coming in and you have to get yourself launched before it gets too low.
If you're on Heroic or Legendary you'll have a Banshee to contend with and it's likely to come straight in on an attack run, but if you briefly take shelter behind the wall it'll veer off (possibly before even firing) and you can then continue; and if you're lucky it'll get distracted by the Pelican. The sheltering only slows you up a few seconds. You may also have to deal with some covies on the bridge of course.
When you're happy with the position of the Shade and you think it's time, do the Shade launch so you get sent flying over towards the Pelican while it's still quite high. There's doubtless some variation possible in the actual launch technique, but in his original video Ms. Man did it as follows. From up on the barrel, throw a plasma low against the wall and then also a frag. Jump backwards off the barrel and then jump up to get into the forthcoming path of the Shade. The collective grenade blast sends it flying your way, and as it arrives you'll need to be doing a press of the X button to prevent yourself being killed by it (hitting X when able to flip a Shade gives you immunity). I believe the standard technique is to press X repeatedly and rapidly, rather than trying to time a single press.
With any luck you end up flying off towards the Pelican. Use drift to help yourself land on the top (you might need to land close to the nose to have enough room to slow down), and then try to get things under control. You'll tend to bounce up and down and can lose health, so it may be tricky. On Heroic and Legendary you'll probably also have that Banshee to deal with, so it's good to have a pistol handy. Once the Pelican gets close enough to the ground you can just hop off.
Ok, now let's return to the matter of killing a Grunt to end up with two plasmas near the Shade. There's no preparation work shown in Ms. Man's video, but apparently he shot a Grunt out of the Shade. Initially I found it difficult to get a Grunt into the Shade, but then I found a method. Pause before the final black stripe in the passage and eventually a Grunt will wake up to man the Shade, something you'll be able to hear (and also detect on your tracker). The Pelican will only be triggered once the door opens, so the long delay doesn't matter.
Another idea is to simply to kill a Grunt at the Shade while he sleeps - assuming there is a Grunt there. But maybe the grenades tend not to end up in a good position? I'm not sure about that as I'm still getting to grips with the launching. But if you don't think it works well, you could instead wake him and possibly drive him in some direction or let him come towards you before killing him. You can exert some control over where the dropped grenades end up. I'm still exploring what works best though, and may be able to update the page later with better advice.
Note: it's best to have four plasmas when you reach the bridge, to avoid the danger of inadvertently picking up a plasma meant for launching.
If you want to get a Grunt who's by the Shade and who has two plasmas, here's a routine you can use to try and minimize how long it takes. But on Heroic or lower it seems quite rare to get a suitable Grunt (I had to give up on Normal after dozens of tries, and I'm not sure how much better Heroic is), so you may need a lot of patience.
When you get off the Pelican at the start of the level, eliminate the welcoming party. A checkpoint will be triggered in the long middle section of the passage, but keep it delayed for now. Deal with the room enemies then stop at the first corner of the exit passage and let yourself get the delayed checkpoint. Save it. You're now ready to start making attempts at getting a good Grunt plus a handy checkpoint, as follows. Jump your way along the passage until past the loading point, then stop to let yourself get the checkpoint you triggered right after the first corner. Outside, the four Grunts have been randomly spawned and maybe you've got a Grunt on the near right with two plasmas. You'll soon find out (he may drop none at first, in which case keep reverting until you see how many he's got). If you hit the jackpot, you'll be ready to make repeated attempts at the main work. If not, eject the disc and restart from the saved checkpoint to try again for a suitable Grunt.
Difficulty and system differences
Extremely difficult! To stand much chance at this, I think you'd need to be pretty good at Shade launching and it would also take a lot of attempts. With my PAL system I still haven't managed it but I haven't given up. I'm not even sure it's possible with PAL, but at the very least I think it'll be harder. The lower power of drift will surely make it harder to drift yourself onto the Pelican, and once you make contact the weaker power of traction would make it harder to stop yourself in time, if it can even be done at all. If I ever manage to land on the darned thing, maybe I'll find out. But in the meanwhile I can't say it's a suitable method for PAL.
History and links
This spectacular method is due to Ms. Man who showed it in Game Over, advertised in the High Impact Halo forum in October 2004. It's also available on YouTube. The relevant footage (done with NTSC) begins at 6:38. The preparation work isn't shown - things start from the launch of the Shade - but Ms. Man told me he shot the Grunt out of the Shade and punched the Shade into position, and that it was probably done on Normal because that's what he almost always used for tricking.