RAGE

As has been said, this isn't overly more difficult than the original hardest difficulty, Nightmare.

A few tips, really, are all you need to succeed, as the game does a good job of helping you along.

-Stay in cover and try to shoot enemies through gaps in that covering (pipes, cracks in the wall, etc.)

-Go for headshots when you can, to conserve ammunition and make the enemies go down faster.

-As far as what weapons to use, I found the Fists of Rage (extra from the Anarchy edition, thanks to bytyqi for bringing it up!) to be helpful in conserving ammo at the beginning of the game, especially against the Mutants who don't shoot at you.
-I also really liked using the assault rifle (with feltrite rounds) and the authority MG (with AV2X rounds). I found that the regular ammunition wasn't even close in comparison to the effectiveness of the feltrite and AV2X rounds, especially towards the end of the game.
-The nailgun is also hugely helpful (thanks MCoreBE for bringing it up!), as the rebar rounds will kill most enemies with one hit, and the railgun slugs can shoot through walls and kill multiple enemies with one shot. However, it will require you to play through the first mission of the Scorchers DLC, which is not required for this achievement.
-Cerichsen also recommends using the Fat Momma ammunition (it will require you to obtain the schematic) for the Pistol and the Pop Rockets for the Shotgun, as well as keeping a few Sentry Bots around when things get sticky. (I preferred to sell everything I didn't absolutely need and it helped me stay stocked up on good ammunition, but you'll have to find out what works best for you).
-(Any of the special ammunition is extremely helpful)

-Try to keep a healthy supply of bandages and don't be stingy with using them - they only run at about $14 in the stores and it can save you a lot of hassle from having to reload/waste your defib over and over.

-The enemies that shoot you are your friends! The only problems I had where the melee enemies that rushed you and the heavys, which just kept on coming. When the enemy takes cover to shoot at you it gives you time to analyze the situation and figure out what you want to do.

-Find a way to make money to buy supplies! I used the Tombstone minigame a lot. SAVE right before you start playing, bet the maximum amount ($25) and try to kill all four before they get to you. If you win on the 10x or 4x round, back out and save again. If you win on the last round that's fine, as you at least keep your money. If you lose, load your saved game and try again. It may not be the fastest way to make money, but it doesn't require any consistent skill to win and it helped me buy the armor upgrades as early as possible.
-Cerichsen said that if you are willing to play through the second Scorchers mission, it will unlock Jackpot in Wellspring and he made between $5000-$7000 from the video poker game in about 30 minutes.

-I didn't bother with any of the side missions or collectibles, as I had already gone through and gotten 100% prior to the release of this DLC, but if you are going for the 100% just remember to be careful and take it slow - it may make you feel like it takes longer than just running through, but all that "time you save" quickly goes into the negative when you end up having to reload to try it 4-5 times.

-This is for the campaign that came shipped with the game - it does NOT require you to do the Scorcher DLC add-ons.

-****This achievement has been confirmed to be stackable with the other difficulty achievements**** (Thanks and congrats to X InFlames80 X)

Please feel free to add comments for any way I can make this better - I'm not putting a full mission by mission walkthrough as those are easily found on the internet, and these were just a few tips that helped me make it through the Ultra-Nightmare mode.

MCoreBE is uploading a FULL playthrough guide of Ultra-Nightmare difficulty. Link below:
http://www.youtube.com/playlist?list=PLFYg0IPAUNeAgybjGzE6HK...

Desert Spores can be found using this guide : http://rage.wikia.com/wiki/Desert_Spore

Using Desert Spores and Night Blossoms you can make Apophis Infusions which permanently increase your max health. With the final mission of the Scorchers DLC you get 4 more hidden at the start of the temple, which means you can create 9 Apophis Infusions yourself, and with the Fabricator or Crimson Elite Armours, that will result in +99 Health which will cap you out at 199 Health for the game. I highly recommend visiting Crazy Joe's swamp as early and as often as possible to harvest Night Blossoms as they only randomly respawn after you complete a Quest/Mission. There are 5 potential Night Blossoms between the entrance to the swamp and the crater (with the 2 Desert Spores in it) so be sure to check them all. You can also buy Night Blossoms, once you reach the Eastern Wasteland, from Jani's Supplies, but they're obviously way more useful early on, so I just harvested them until I had what I needed.

As for what qualifies as a Quest/Mission, yes, even the DLC Sewer Missions count, both times you clear them, so abuse the system as necessary.

And speaking of those Sewer Missions, remember the first time (and only the first time) you enter Kvasir's Sewers near the Northern Watchtower, there is an early obtainable Rocket Launcher under the stairs that lead to the exit. Pick this up and you've got an even greater advantage.

Don't forget the ID Software collectables like the Wolf Goblet + Quayola Quayons (Ghost Hideout), Shambler Plush (Wasted Garage) and Pinkies as these can really help out early on with money troubles and I cannot stress enough how good Video Poker is for earning easy money. By abusing it, you can max out on anything you need, whenever you need it. Also, as a general loadout, the Rebar Nailgun with Sentry Bots and Wingsticks make for a very easy time of it.

Edit : To clarify about infinite money, you need to have The Scorchers DLC and have access to Jackpots which is only possible after clearing the Scorched Refinement DLC Quest. The Video Poker machines have great odds and a good payout ratio provided you have a good eye for Poker. It's very generous and often you can see a winning hand coming, so just practice and you'll soon see the huge returns.

However, without the DLC it is still possible to gain huge amounts of money/ammo, it's just a bit more complicated and a lot more time consuming. To do it without the DLC, you need to locate either of the 2 groups of people playing Tombstones (1 is between Coffer's Outfitters and the Job Board in Wellspring, the other is down the stairs to the Racing Track in Subway Town). Simply save your game and play Tombstones. If you win save, if you start to lose too much, reload your save. Remember to keep several different slots and alternate your saves with this method. As for ammo, just keep replaying Mutant Bash TV. You can get a good amount of ammo and it's not too hard. Even better is that it's free. I hope this helps to clarify anything anyone may not have known or understood before.

The mission in Capital Prime was a breeze, I had max Av2X rounds, 1000+ for the Pulse Cannon (and 20+ BFG Rounds), over 200 rockets, 90 Bandages, 50 Advanced Sentry Bots, 99 Advanced Wingsticks and whole load of everything else. Also the Railgun is great for when you're injured and up against heavy opposition.

All in all, a very fun third playthrough for me, and a very easy Achievement.

Including the Scorcher missions in this DLC but skipping all side missions and other achievements not in this DLC, it took me about 12 hours to complete the campaign on Ultra Nightmare. The Scorcher missions themselves take about 2-3 hours and take place through the first half of the game (before you go to Subway Town).

The biggest changes to Ultra Nightmare over Nightmare are:

The price increase for supplies.
The amount of items made per recipe.
The amount of damage taken when shot.
The difficulty to win races (the time limit on the first race in Wellspring is 1:28 minutes instead of 2:08).
The duration of time required for Nanotrites to recharge (for your heart defibrillation).

1. If you've completed the game before you cannot just load up the last mission on Ultra Nightmare and complete it to get the achievement - you must play through the entire game again. The achievement does however stack.

2. The cash farming will make this achievement pretty much a breeze. Given you can only hold $9999, make sure you fully stock up on ammo, bandages and ingredients through your gameplay.
2a. In Wellspring, the Roly-Poly load glitch lets you get up to $9999 within about 10 minutes. Example shown here: 2b. In Subway Town, buying Viper Rockets from Stew (top floor, behind Jani's shop) and selling them to Jani will earn you a 13% profit each time. Getting up to $9999 from $1000 takes longer than the Wellspring strategy; about 40 minutes or so. You will be able to buy Viper Rockets after the you complete the first mission (clearing the Blue Station), but not after the following mission (going to the Gearhead Vault).

3. Make sure you pick up armor upgrades (light and medium in Wellspring, heavy in Subway Town) and the recipes (in both Wellspring and Subway Town). Even with the cash farming and a lot of ammo, you will still die quickly due to taking higher damage.

4. Sentry Bots (and after the recipe upgrade in Subway Town, Advanced Sentry Bots) are really useful. While they don't have a lot of armor and ultimately won't last long, they can keep enemies off your back and insta-kill most enemies if they jump on them. Keep enough ingredients on you to craft 5-10 of them for any given mission.

5. Save Often. The autosave checkpoints are less frequent than you would think, and reverting back to a checkpoint can take you 20-30 minutes back from where you died.

6. The Nailgun, obtained after the first Scorcher mission, is a really useful weapon. The Rebar ammo will one-shot kill most enemies (including enemy sentry bots) and has a very long range. The Railgun ammo provides you with a special infrared-like scope that can show enemies even if you have no line of sight, and shoots through walls. This ammo comes in useful for various "bosses" that you will come across towards ends of missions, as well as snipers in the second Dead City mission. Keep in mind that it has a somewhat long reload and isn't good for close quarter combat.

7. The Rocket Launcher is your ultimate buff weapon when all else fails or just need to get rid of a tough enemy quickly (especially Kraken enemies, who can kill you in two hits.)

Overall the achievement isn't too difficult, especially when you farm cash (and why wouldn't you?). Good luck!