Alright, here's the strategies that got me through the Plant extreme boss battles and other tricky sequences. I credit various strategies around the net for some of these (including Gregor's list above and http://www.xbox360achievements.org/forum/showthread.php?t=35...
This list is in no way meant to undermine Gregor's above, but I know it's always nice to have a few different ways to tackle these things and hope that some of my (definitely dodgy) strategies will help someone.
I am an average skilled player, so I hope the strategies below help out someone who may be struggling like I was. Not all of us are uber-elite reflex gamers, so the fact that some of the below strategies may be cheap and dodgy was due to survival and a dedication to completing this difficult (but ultimately satisfying) achievement.
(Note: As with the other solutions, these assume you have already earned the stealth, infinite ammo brown wig and infinite grip orange wig on prior playthroughs.)
Although not really a boss battle, this can still be daunting on Extreme. The solution? Equip a cardboard box and don't stop moving from side to side.
Definitely the most difficult and frustrating boss battle on Extreme for me personally - so don't feel disheartened if it gets to you at first. Let me just say, there's a reason this strategy is probably longer than some of the others... I tried using various strategies across the net and ended up getting the job done with a classic standby - the claymores.
When the battle starts, defuse the bomb to your bottom left straight away and then go nuts placing claymores (with your infinite brown wig naturally). I would usually place 7 or 8 quickly, but in a clear memorable pattern that would allow me to navigate past them easily when chasing the fat bastard.
Once that is done, run over to Fatman, knock him over and defuse the bomb. Quickly run around in front of him and hit him in the head with the socom and trip him over immediately when he taunts you by shooting his rollerblades to get another easy headshot.
The overall strategy from here is to tail him as closely as possible whilst run-shooting with the Socom to chip off his life bit by bit, knocking him over/defusing/headshot - rinse & repeat.
So far (minus the claymores) this is a standard strategy that most people use - but this is where the mines come in. Everytime Fatman would hit a claymore, it would give me a chance to either catch up to his position and defuse a bomb, sometimes even getting a nice free shot in. I found that if he set one off near me, I would always re-plant the mine asap whilst he's down and out.
The hardest part of this fight for me was letting the bastard get too far out of sight and planting too many bombs without interruption. I found that once he'd planted 3 consecutive bombs before I had a chance to defuse once, I had no chance. Maybe some better players could handle it, but I needed to keep up and the mines were key in slowing him down for me.
Lastly, remember that even if you manage to take the bastard down, you will still need to defuse any active bombs. I leapt for joy when I finally took him out for the first time, before I realised there was a bomb with 3 seconds left on the other side of the helipad....
This is one battle where the standard strategy of hanging around the stairs between the upper and lower levels didn't work for me, so I looked for alternatives.
Apart from being quite tricky, this battle was not as frustrating as some of the others and was simply a matter of learning to predict which attack was coming next. This gave me a chance to be in one of the 2 positions outlined below, or in between them at the very least.
The 2 areas I used were the balcony at the entrance to the north shell and the railing on the top left of the central section. I'll be listing off the harrier's attacks and using these as location references.
When the battle begins, naturally grab the stinger, equip the brown wig and get 2-4 free shots off the bat. Now instead of a play by play, here's what I did for each of the harrier's attacks.
This is when you see the glint in the sky and the jet zooms past. Position yourself near the railing at the top left and fire off one rocket when he appears and then hang off the railing - using the invincibility frames of the hanging animation for protection against the missile.
Hover-above exhaust attack
This is perhaps the trickiest to deal with using this strategy, so I usually equipped body armor and then took some minor damage whilst hitting the jet approx 4 times each time it hovered above - a worthwhile sacrifice in my eyes.
Machine gun spamming
When the jet starts spraying the machine gun from all angles, try to be prone in the top half of the balcony behind the wall. It's a little tricky to get the positioning right the first few tries, but eventually you'll be able to cover yourself 100% from all angles without having to bother moving or running around like an idiot in a box on the lower levels. You should be able to get a shot in at the jet once it's finished spamming.
Giant destructive missile
This is the missile which usually takes out half the upper level (but not the area we're using). Just use the top left railing flip tactic once again to avoid damage.
This is when the camera goes side on and the jet fires a multitude of missiles whilst swinging side to side. Use the balcony wall to protect yourself while prone, although it is a little trickier to not take damage then the machine gun. The jet usually lingers for 5 seconds afterwards, so you should be able to get one or two shots in when it's safe. The hardest part of this attack is predicting when it's going to happen, so try to hang between both of the locations in this strategy after each drive-by missile.
Overall, the harrier fight is all about predicting and handling these attacks.
Okay, here's where the dodginess really begins. As seen in many videos around the net, it's entire possible to beat Vamp on Extreme without taking a single hit of damage. I managed to do it first try using this hilarious strategy.
When the fight starts, equip the infinite grip orange wig (yes - THAT one... the one we NEVER use) and hang off the north railing in the room. Vamp will continually walk up to you and proceed to enter into an attack animation. This is when you flip back onto the platform and do a punch/kick combo to knock him down.
Then flip back over and continue this until Vamp is eventually taken down by stamina depletion. Every now and then you may get hit by a stray knife, but the damage is minimal and managable.
Hilariously easy and dodgy~ as all hell - but after 4 playthroughs and Fatman/Harrier on Extreme, I think we all deserve an easy one.
Emma sniping escort at Oil Fence
Not much to add to Gregor's strategy above, except for one thing which helped me.
After a few tries, I managed to learn exactly when and where the soldiers would appear throughout the sequence. Coupled with an increased brightness setting on my TV, meant that (apart from the claymores), I didn't really use the thermal goggles at all.
You know what that means? INFINITE AMMO SNIPING BABY~!
In all seriousness, the PSG-1 is almost semi-automatic in it's firing rate, and if you completely suck at MGS2 sniping like me, then being able to fire off 5 bullets at each enemy without having to worry about replenishing ammo is a godsend. During each little 'quiet period' I would also use up the remainder of my clip to ensure I didn't need to reload during a crucial moment.
Lastly, although you certainly have to position yourself to the side to hit the hidden claymore behind the post, I positioned myself back in the centre immediately afterwards as I preferred the angle. I'm not certain if this is a disadvantage for Vamp or not, but I managed to take him out first try regardless.
Hallway Tengu battle
I doubt there's a better strategy then the one listed by Gregor above. I personally used the Stinger to clear out all enemies until the last section, where it almost seems like a necessity to tranquilise Snake to keep the stupid bastard from rushing in Leeroy Jenkins style and getting himself killed. Using coolant on the sword tengus and finishing them off with a gun (I used the socom) whilst ducking behind the crates will eventually get you through.
Circular room battle
I stood in the doorway where you entered from and used the M4 with the brown wig and just kept mowing them down. I tried to focus on the gun tengus first and any sword tengus directly near Snake. Again, your success in the section primarily relies on Snake not being a suicidal nut (seems to be a trend) and running directly into your gunfire, so it may take a few tries because of this. The tengus will most ignore you and focus on Snake, but you will need to take the odd one out that is stupid enough to run up to you.
If you can avoid using any rations in this section, then it may help you out during the Ray battle, but it's not absolutely necessary to have any.
Metal Gear Rays
Oh boy... be prepared for a long and draining fight. To be honest, I enjoyed fighting the Rays - I just hating getting through 15 or 16 of them and getting killed in one hit by a stray missile.
As in Gregor's solution, there's no easy way out. Your survival hinges on a few things:
1. ALWAYS have a Chaff grenade going at all times
This means that the overhead missiles will hit the where you were standing when they were fired and not home in on your current location. I cannot stress how much of a life saver this is. After 2 or three hits on a Ray, I would always throw a new Chaff to keep it going.
2. Distract the sidelined Rays
I found that after hitting the central Ray (standard knee/head combo), I would usually fire a random stinger off at a Ray on the sidelines. Even if it hit them in the knee and did no damage, it provided a distraction and often delayed attacks. After working this into my routine, I would often hit a sidelined Ray when they were 'screaming' by chance, which dealt 1/3 damage.
3. Memorise the movements and sounds of the Rays so that you know what attack is coming
As mentioned in the other solution, AVOID THE KNEE MISSILES. Although I managed to dodge them most of the time, sometimes they would come from a strange angle and they pretty much kill you with one bloody hit. I found that staying at a medium distance and running diagonally away from the central Ray often caused him to use the machine gun attack instead, which is by far the easiest to dodge. Eventually you'll also get used to when the laser/water beam attack is about to fire, which I would dodge by cartwheeling diagonally backwards.
4. Don't panic, don't take risks and stay concentrated for the long fight
This may sound ridiculous, but I think it's very important for this battle. Quite a few times I got up to about 15 or 16 Rays defeated and started taking risks - firing more stingers at a time, not keeping the chaff grenades going, etc. Everytime I broke away from my pattern, I paid the price (usually by way of knee-missile). As in Gregor's solution, sometimes the Rays will be unpredictable, so of course you have to adapt, but I think it's very important to stay focused, especially as half of the attacks can kill you in one hit.
...and lucky last. Time to be complete dodgy~ again!
As you are well aware by now, there are 2 parts of this fight:
This is the easy one. First off, equip body armour (I had this equipped the entirety of the battle). The dodgy strategy for the first part is very similar to the Vamp strategy above. Hang off the building on the right side of the screen. Each time Solidus walks over to attack you, flip back up and hit him with your sword combo. Rinse and repeat until this section is over. 90% of the time his missiles will fly over your head, but keep an eye out on them and flip up quickly if it looks like their angle will hit you.
Ideally, you will want to get through the first part without taking any damage, since the second part is much more unpredictable.
Hopefully you still have most of your health left thanks to the dodgy~ strategy above - and you'll probably need it. Many other strategies on the net (included Gregor's above) involved blocking/countering/some other ninja stuff.... but I found the hit-boxes and sword controls too sloppy and inconsistent for me, so I modfied my cheap strategy from the first part.
For the second half (still with body armour equipped), I stayed down the bottom of the screen and waited for solidus to boost towards me. As soon as he was close to hitting, I would flip off the edge, which would cause him to miss. As soon as he gets out of that attack animation, he would usually begin another attack (usually a combo), which would give me a chance to flip up and hit him with a sword combo. Be warned that he will often try to kick you instead of a combo, so I would usually hold the block button while flipping up just in case. If you manage to hit a combo on him, he usually then farts about with his fire-trail boosts before coming at you again.
I found mixing up the 'dodge-off-edge-and-flip-up' strategy with one that simply involved dodging to the side instead worked for me and I managed to take him down after about 4 or 5 tries. As I said, there are more effective (and flashier) strategies, but the sword controls just didn't gel with me, so my dodgy~ strategy had to suffice.
Alright - I hope this long-winded solution helped somebody out. Please don't leave negative feedback due to the cheapness of some of the strategies. As I mentioned at the start - not everyone is a pro gamer, and after putting all the hard work into getting the dog tags on the previous 4 playthroughs, I think some people might just want to get through these hard battles any way they can.