Here's the rub, folks: this is not an easy achievement, as the ratio proves, but it becomes easier if you can make it to Skyhold. The above solutions are fine and dandy, but I decided to go with two mages (myself as a human [this will help later with armor available in the Hissing Wastes, but that's up to you] and Solas), one ranged (initially Varric and then Sera once her bows become stronger than Varric's Bianca), and one tank (initially Cassandra and then Iron Bull once he gets a superior two-handed weapon). Two mages will allow you to maintain a barrier for the major part of most battles, and this was something I found critical to succeeding on nightmare difficulty. You can essentially alternate between yourself and Solas with casting Barrier when necessary (which is all the time) and this will greatly increase your chances of success. You should also focus on increasing the guard of your tank via belts and/or masterwork items once you acquire them. This won't make him unstoppable, but he'll at least keep the pressure off you for longer, which is crucial.
For the most part, you're going to be focusing on completing main story missions, with some asides that will help you level up (and overlevel, in some cases) in order to make the game slightly less challenging. Now the first thing you need to do is focus on upgrading your Barrier spell for your primary character and Solas. The initial spells that you start with (Chain Lightning and Flashfire) will suffice until you get to Skyhold. If you can spare it, I recommend getting Dispel, which is super useful in closing those glowing green holes that accompany rifts, and for reducing enemy barriers. It's also worth noting that Demons are susceptible to ice more than anything else, and this might be extremely useful during the most challenging part of the game, which is the siege on Haven, in my opinion.
Now you might be wondering about Inquisition Perks. First off, the exploit to max out your Influence and therefore the perks no longer works. Ruh-roh. In any case, I highly recommend that you take any two or three codex experience perks, preferably prior to exploring Val Royeaux (there are a bunch of codices laying around here for some reason, enough that you can get a sizeable chunk of XP at this early juncture). Then, I recommend the perk that gives you access to some pretty decent mage equipment, including the staff and armor you'll use for the majority of the game. This one makes the most sense since you'll be saving the world with two mages, and you might as well have them decked out in superior gear. You will also greatly benefit from increasing your potion capacity and, if possible, the extra potion slot, as soon as possible. 4 extra healing potions make all the difference in a lot of battles, as do rejuvenation potions. Other perks are up to you, but I recommend taking 10% increase to all defense as soon as you can after capturing the keep in Crestwood (you have to capture the keep to unlock the perk option; unfortunately you can't do it until after you've reached Skyhold). I also recommend the retroactive research item XP one at some point. Speaking of, collect and turn in research items as much as possible, as you'll gain experience and damage increases to the respective enemies this way, which is always good.
Okay, so here was my path to success:
1) Save frequently. This goes without saying. The last thing you want to do is replay 15 minutes of difficult gameplay because the 5-second save process was too inconvenient for you. As an added note, you can absolutely do this achievement on your first playthrough, so that's up to you.
2) Complete all the quests you possibly can in the Hinterlands. I don't recommend pursuing the shards here or anywhere in the game unless this is your sole playthrough, as the accompanying perks were ultimately unnecessary for me after I achieved my class specialization. More on that momentarily. Your goal is to reach level 11, or 12 if possible, prior to the siege of Haven. You should also have the best possible armor and weapons for all of your characters prior to the siege.
3) Speaking of, improve your weapons, your armor, and the respective weapon/armor add-ons as frequently as possible.
4) The Siege of Haven is a pain in the ass, and probably causes a lot of people to give up and/or break their controllers. Rest assured, the game gets dramatically easier after this point, so hang in there and keep trying. Most of the siege isn't especially difficult; just hang back and cast spells while the rest of crew distracts the enemies. Obviously, heal fully before replenishing your supplies. During the first two ballista sections, focus on cranking them while your buddies take care of the enemies. Only break to make sure your barrier is intact. I made it through all of this without dying or reloading, so it's not that rough. The real challenge will come during the penultimate battle of Haven, when you have to crank to final ballista. This is a really tough section, and you will likely die multiple times. Make absolutely sure to leave the crate of supplies right by the ballista until you absolutely need them, and to help yourself out even more leave a crate of supplies by the main doors to the Haven chantry, just in case. Speaking of, don't be afraid to retreat away from the ballista if you're overwhelmed and your buddies are dying off like idiots. They will transport next to you after a certain distance, and you can revive them easier this way. Also, there are two things to note about this battle: you can save between waves of enemies, which is nice, and a new wave of enemies will arrive each time you start cranking the ballista handle. For this reason, make sure to crank that damn handle (insert lewd joke here) for as long as possible before attacking enemies. I highly advise that you focus on this act instead of attacking enemies, because once it's complete the battle is over. With a little bit of luck you'll persevere and get to Skyhold. And just to give you a sense of where you should be at level-wise, I was at 11 when I attempted this, and it was challenging. Unfortunately, I think it's probably fairly difficult to get higher than this without some really serious grinding.
*** EDIT: Rhyolitic adds this about the Siege of Haven: [For that final trebuchet (not ballista - ballista are basically giant crossbows, trebuchets are counterweighted catapults), crank just enough that it spawns 2 enemies. Take them down, then continue cranking till the next group spawns. If you try doing as much as possible, you'll probably get overwhelmed. I was able to do this at level 9 w/Iron Bull, Solas, and Varric.] ***
5) Once you've made it to Skyhold your number one objective should be completing the class specialization quest for the Knight Enchanter. You will likely have acquired the Wisp Essences you need if you played through the Fallow Mire map (which you should have), so you're good there. If not, head back and fight until you have them. As for Lazurite, unlock the Hissing Wastes map and then head back to Skyhold. Go to the War Table and you should now have the "Hissing Wastes Resources" mission available. Keep doing this until you have 10. Alternatively, you can try to traipse around Hissing Wastes to collect the lazurite on your own, but be forewarned that the enemies here are all at level 16, and will likely kill you quickly. The final item, the book related to the Knight Enchanter quest, is located in the Skyhold room with Vivienne. Once you have all three, craft the Knight Enchanter hilt and turn that bad boy into Commander Helaine. Welcome to the best class in the game.
*******EDIT:Sakori says: "As of today [Sept. 9, 2015] Knight enchanter has received a very major nerf in spirit blade. Damage is now halfed and it lost most of the bonus damage vs guard/barrier.
The class is still pretty strong, but you can't just spam spirit blade anymore. Other spells (like barrage or fire mine) get the job done just fine." So it appears an update has made the Knight Enchanter far less powerful. I think it'll still prove to be the most useful class for the Nightmare playthrough if you use Sakori's spell tips. END EDIT*******
6) You might be thinking, wait, this puts me right in the fray. You're damn right it does, but you'll be nearly invincible while you're there. As soon as you can, acquire the spirit blade skill and it's second level option. You'll be using other spells throughout the game as needed, but this (along with barrier) will be your bread and butter. I highly recommend you lock all the other skills in this class tree, with the exception of fade cloak and resurgence. If you have to, use the blacksmith's shop to purchase the item that allows you to reallocate your skill points, keeping all skills that relate to barrier, putting all your points into knight enchanter, and keeping something like chain lightning and an ice spell around for the fade rifts. Now, the beautiful thing about the Knight Enchanter is that using spirit blade renews your barrier at a pretty decent rate, so as long as you're swinging away it's really difficult for enemies to hurt you unless they have some kind of armor / barrier penetration capability or you get knocked down. Suffice to say, I almost never had to heal once I unlocked Knight Enchanter, and would often find myself fighting on as a lone ranger well after my buddies had fallen unconscious. This was true in dragon fights and with several of the more challenging fade rifts, just to give you some sense of how overpowered you will become. As another note, you do bonus damage to enemy shields and barriers with Spirit Blade, making it hard to lose.
7) Play through the game normally now, making sure to be at the top end of the recommended level for each story mission. One thing I recommend is acquiring awesome crafting materials in the Hissing Wastes (lazurite and volcanic arum) and Emprise de Lion (silverite and dawnstone). You can also go for everite near the dragon in the Emerald Graves, and get august ram fur and great bear hides here. All of these things are great for crafting. Once you hit level 12 and/or have your Knight Enchanter in full-blown beast mode, you should be able to tackle more advanced areas and enemies, like the level 16 enemies/rifts in the Hissing Wastes and Emprise de Lion. I don't recommend trying to revive your buddies if they die, as they'll just suck up healing potions and usually die again. Anyway, our goal now is to acquire around 9000 gold to buy the best armor from the Canyon Shop in the Hissing Wastes. And by best I mean the heavy armor. You might be thinking, but wait, only my tank can equip that! Wrong. If you use silverite to craft armor it removes the race limitation (and fade-touched silverite removes the class limitation; thanks EbonHawk01 for that tidbit), so now your mages can enjoy an even greater defensive boost. Also, if you complete the various tomb puzzles in the Hissing Wastes you can get fairly nice schematics for yourself and other characters that will make life much easier.
8) At the same time you're doing this you should be pursuing the sidequests associated with Iron Bull. I don't think you can complete all of them until after the Wicked Hearts / Orlesian court story mission, but you can always get the ball rolling. Now this part is very important: when you are given the sidequest to accompany Iron Bull in the Storm Coast, you must decide to sacrifice his men and save the dreadnought. The reason we're doing all of this is to get the best staff in the game, the Masterwork Archon Staff, and you won't be able to do this if you choose to save his men. Eventually you'll be able to choose a number of spy missions from the War Table. They will take a while to complete, but they are totally worth it. This is the final mission you must complete in order to get the schematic for the staff:http://dragonage.wikia.com/wiki/Track_Spies_in_Vyrantium
(Obviously this is property of the Dragon Age wiki)
You can backtrack through all of the previous spy missions through the above link, so you know exactly what to do, who to send, and how long it will take. It helps to have acquired as many agents as possible, as they will reduce the mission time of your three main advisors. Up to you. If you like, you might want to search the same wiki for the best staff blades and grips. That's getting a little too nuanced for me, so I won't include that here.
9) Have fun! You can totally kill dragons without fear once you've become a Knight Enchanter, especially after you're level 14 or so. That's when I took on the dragon in the Hinterlands, followed by the one in Crestwood, Emerald Graves, and Hissing Wastes. You can go for more if you want, but I was really focusing on just beating the game after I killed these four (I had already killed all 10 in my first playthrough). Obviously the dragon blood and bones they offer are very nice for crafting purposes, and they also provide large chunks of XP. This is optional, though I found it useful. I didn't struggle against any of them, even as my companions lay uselessly beside me, dreaming of being as good as me. As a final bit of useful info, I was at level 19 when I completed the game, and, having done everything in my first playthrough in about 85 hours, I streamlined this playthrough to complete the game in 44 hours.
If you have any questions or comments for improving this guide, don't hesitate to let me know!
*** EDIT: Solution has been modified to reflect information on the Amulet of Power exploit that has been patched since the solution was originally posted. ***
*** EDIT 2: Information added and corrected to reflect comments by EbonHawk01. ***