Ok, all these solutions have good points and the video walkthrough can be helpful for sections but let me break it down level by level with a few bonus tips. I beat extreme in 2 sittings and just under 8 hours, I was able to complete 3 levels without dying and really found the extreme challenge not to be so extreme.
First Tips: Why I haven't seen these mentioned before is beyond me maybe no one knows or people are keeping it to themselves to keep a high ratio.
Invicibility yes as Seraphim stated there is a invincibilty frame when you roll, but how would you like 2-3 seconds of invincibilty, sadly you cant do anything but you dont take damage either. Everytime you get in and out of your VS you are invincible. Are you in a VS and about to get hit by rockets hop out and wa-la no damage then hop back in and continue kicking butt.
2. Plasma Rifle for Extreme it is a must not only to get hard to reach target markers but it is extremely powerful, takes down Akrid and VS easily and can zoom in. If you can get one keep it.
3. On the subject of weapons, learn to love grenades they are fantastic, I personally only like the hand grenades, because they are plentiful and you can hold 20. Don't waste time shooting Therm tanks just chuck a grenade so when you arrive at where the tank used to be you can grab and run. They also work great at taking down VS's anywhere between 4-6 should take down all but the most hardened VS.
Extreme is about survival not wiping out Akrid, Nevec and Snow Pirates, if you can skip them do.
4. Never leave a VS without it being blown up, it is just a waste of Therm - E, If there are extra VS's around hop in and let them get blown up. If you already killed everyone then use a rocket launcher or grenade launcher attachment and do it yourself.
5.While VS's are great and you will be spending a lot of time in them, they suck you Therm - E like no tomorrow, so if you dont really need it get rid of it and hoof it.
6. If you haven't played in a while play through once more on easy or normal to get re-aqquanited with the levels, in extreme getting lost can be the difference between life and death. Most levels you should be able to complete in under 30 minutes.
Ok now that you have some basics I will go through a level by level and boss by boss breakdown to help you through the toughest parts of the game.
Level 1 - Nice Introductory Level Simple enough, actually this is probably the hardest level on Extreme. Basically you want to gather as much Therm as you can and run to the boss, the VS you get at the beginning, let that first big Akrid demolish it for a nice 1200 units of Therm, grab all the tanks and exploding barrels you can and run. I was able to beat the boss with only 900 Therm, but you dont want to do this, ideally you want to have at least 2000 Therm before you face him; mainly because he is probably the toughest boss in the game. The only real tips I can give for beating him are when he balls up to roll hit him with a frag to take him out of it and shotgun the hell out of him. Oh yes and deal with those 4 pesky minions first, with them out of the way he really isnt that bad.
Level 2 - Run Run Run, the beginning of this level is brutal, blow up all the cars and barrels you can to collect as much Therm as you can before you hit the 1st open area and start spawning enemies after this just run to the tunnel for a checkpoint hopefully, you made it with 1000 Therm but if not the rest of the level is pretty easy and you will have lots of chances to gather Therm in the upcoming sections. The boss on this level is not too difficult first take out his two VS henchmen I like using the Rocket Launcher on top of the building on your right when you start to take them down and then finishing the job with the shotgun, by the Therm tanks. Once you have the boss by himself run to the other side of the level and use the building in between the single and double therm tanks as cover, and then just wail on him with rockets.
Level 3 - The Ultimate Run level grab all the Therm you can at the start before the Worm spawns and then run like no tomorrow to the junkyard. This boss is a joke if you know two things, the first is jump, most VS's in the game regular or boss wont fire at you when you are in the air, simple enough or if you want to be really cheap, use the VS invicibilty trick, hit her with a rocket and then hop out and back in your VS, then just rinse and repeat til she is done for.
Level 4 - The level is pretty straight forward grab all the Therm you can and high tail it to the boss. Ok now this boss is my least favorite and the one I found to be most difficult until I discovered a neat little trick. Yep you guessed it the VS invincibilty trick, you dont need it so much for the first half of his life but you will for the second, just nail him with rockets and missles, until he starts to go agro, now for the second part of the trick, when he flys way off in the distance to zoom in at you move behind the pillar in the center. When he does charge he will hit the pillar at it will stun him long enough to get a rocket or a couple missles off, then go back to using the VS trick til he charges again. This will be the last difficult boss fight from here on out you should be on easy street.
Level 5 - No special level stratgies just grab all the Therm you can make sure you destroy all but the last VS in the level, if you make it with more than 2000 Therm it should be an easy fight. This boss is really too easy, you will want to use dual gatling guns for the entire fight so stock up on ammo before you get there so you arent wasting time searching the arena. The main thing you want to do is make sure that once you get rid of the first arm, that she never is allowed to have two arms at the same time again. It will be tempting to just wail on her head until she starts to grow her arm back but dont. Get rid of one arm and then 3-4 seconds on the head then start working on her other arm, once she has grown the first one back, the second should be ready to come off. When she is almost dead about a 1/6 of her life left just shoot the stalagtites above her head for a quick easy finish.
Level 6 - Again grab all the Therm you can Remeber leave no VS un-destroyed and high tail it to the boss. Good old Green Eye, you fathers arch nemesis, well he wont be yours, for the first part of this battle you are going to want to have rockets and a gatling gun, you can go about this one of two ways:
Chase Green Eye around the buildings shooting the yellow pods on his sides when you have the oppurtunity or you can let him chase you. Either way makes no difference just keep using the Y button to make use of the dash feature and keep pounding his sides until all the yellow spots are gone. It is advisable not to try and jump around too much when fighting him especially when he shoots the ice at you as you may inadvertently run into it. Once you have destroyed his sides jump up on the buildings and swap the gatling gun for a grenade launcher then just one or two well placed grenades should end this fight very undramatically I might add.
Level 7 - This is one of the few levels where you are going to want to follow a very specific pattern of how you do things, Beer Baron video walkthrough is an excellent guide to how you should proceed through this level and what weapons you should pick up hint the Plasma Rifle is going to save the day. Once you have gotten to the boss dual shotgun him to death which should take only about a minute, why are the VS bosses in this game so lame. Oh well onto level 8.
Level 8 - This level has a ton of VS's in it so having a lot of energy to face the boss should be no problem not to mention that there are a ton of tanks in the boss stage anyways. A few tips leading up to the boss. You will want to kill all the VS's leading up to the boss, i recommend using a EM Laser and Shotgun combo, stun and spray they wont know what hit them. Once you have dealt with the last 3 VS's gather all the rocket ammo you can find, this next boss is a tank literally but the rockets arent for him. When the boss fight starts you will be facing 3 of the little tanks and the boss one very large tank, use the rockets you gathered to take these three down. Now you can go at this boss one of two ways use the remaining rockets you have to shot him then switch to a grenade launcher or shotgun until he is dead fun but to much searching and dodging, oh and by the way dont bother hitting him in tank mode only hit him in spider mode, otherwise you are wasting your ammo. Preferably a much better and safer method for finishing this boss is my favorite weapon yep the trusty Plasma Rifle. You probably dont understand how a little plasma rifle can take down such a large opponent but it does, I couldn't figure it out either. Anyways in once you clear out his 3 minions, look on one of the circular platforms for the Plasma Laser then, jump up on the raised section with all the Therm tanks and just start shooting, he can't hit you up here with anything except his cannon and you will see that coming from a mile away and can just jump out of the way. Boss 8 dead.
Level 9 - This level it is extremely important you have a lot of Therm going into the boss fight, since the Therm he drops can sometimes be tough to get to. I had 4500 going in and was still struggling to keep enough to stay in my VS. Anyways do the same thing during the level you did in all the others, this level probably more than any other you want to avoid conflict as much as possible. Only really engage large enemies or enemies to help you destroy your VS. You have a choice on what VS you can take against the boss you can use a tank VS or a VS like the one you used in the Green Eye fight. I prefer the tank VS for this fight since you dont have to bother looking for weapon attachments you can get straight to business. Use the tank VS in spider form and put two cannon shots in each of his front legs. Once he goes down jump and hover put two more cannon shots in his back, jump hover and two more. By this time he should be growing his legs back just rinse and repeat twice more and then its all over.
Level 10 - This is one of the few levels that I actually suggest fighting as many of the large Akrid as you can, in the beginning it will be tempting to hop right it that VS but it will suck your Therm way to quickly, preferablly let the scorpions jump up to you and then kill them with 2 quick grenades and a few machine gun rounds. Once all the Scorpions have been dealt with hop in the VS and jump across the road to grab a shotgun attachment, by this time 2 dongos should have spawned. Lay into them then grab the Plasma Rifle on the far end of the roadway and proceed quickly through the next 2 tunnels and into the city section. In the city section you will want to take down both of the large spider akrid, as well as destroy your current VS and the one sitting up on the tunnel entrance, since you wont be needing any VS's for this next boss fight. In the room right before the boss hop in that VS and destroy it, then on to the boss fight. If you did killed everyone I mentioned quickly and efficently then you should arrive at this boss fight with 3000 or more Therm which will make it a piece of cake. When the fight starts stay against the walls with the weapons, he slam his tentacles down 3 times just before he slams it down a 3rd time toss a grenade when the end of it was landing and then add a couple Plasma Rifle shots. Then crawl into the hole he retracted his tentacle into and shot his sweet spot. You need to do this twice for each tentacle. After the first tentacle is gone he will start to spawn those annoying flying akrid from two holes on the left and right of his stomach, one good shot from the Plasma will put an end to that, though they will regenerate after some time. He will also spawn some electrifed jelly fish looking things once again a couple of shots with the plasma and no more problems. Once his tentacles are gone he will open his mouth to reveal his real soft spot lay into it with a couple rockets and keep on the move. If he starts spawning more flying akrid or jellyfish, just switch to your plasma clear them out and returning to rocketing his tongue.
Level 10 Part 2 - Thats right levels not over one more boss fight til the final boss, but this one may be the easiest in the game, you should have no trouble getting Therm in the 2nd half due to about 50 VS's laying around everywhere. Anyways you will want to have at least one shotgun when you go into face the boss, you can grab another on his stage and then just go to work. 45 seconds to 1 minute and he should be done for, just circle and shoot him, and if he starts spinning his drill arms jump out of the way.
Level 11 - This is it Final Boss, he can be terribly frustrating if you dont know what to do, but once you know his pattern easy as pie. When you start off you want to start pummeling him with little blue disks, until he calls, his first cannon to assist him. Once he does this you will want to change to getting in close and slicing him up everytime he bends his arm. Once he calls in his 2nd cannon, back off and go back to shooting disks at him. You only want to attack know when he starts his orange slicing manuver, wait until the 3rd slice, the one that goes round in a circle then dart in and slice him yourself. After about 5 minutes you should be an Extreme Soldier.
If you have any questions or would like any help on any specific parts dont hesitate to shoot me a msg here or on live.