** Possible Small Spoilers Below **
Nightmare Mode is the same as the Story mode except the Game no longer Auto-saves (meaning if you die you start back at the last time you saved the game which can be a huge headache!) and also you have less time to complete the game before the bomb goes off (2 in-game days less).
I do NOT recommend this mode for your first play through unless you are a veteran of the series and know what you are in for.
My tips for completing this without any trouble:
1) SAVE OFTEN! I cannot stress this enough, because if you die you can lose a whole lot of progress and may cause you to throw your controller at the wall.
The Easiest way to do this is to look at the map and go to the closest safe house you can find as they always have a save point in them, this is far easier than trying to locate one elsewhere.
2) Be level 50 with all attributes upgraded fully and also have unlocked the combo weapon abilities where you can combine almost anything (Note: You will have to have a fair amount of blueprints).
This isn't required but is strongly recommended as this gives you perks like regenerating health, indestructible vehicles and so forth.
3) Always have a range Weapon (I always used the Z.A.R which is just two guns combined), A Good Melee Weapon (any will do, just combine any combination of knives/blunt weapons) and an Energizer Drink (this drink makes you invincible for around 4 minutes, just combine 2 soft drinks to make it however you must have unlocked the ability to combine drinks/food in your attributes panel).
Keep this drink until you really need it or use it when facing bosses to make them a breeze, very easy to remake as well, just go to any fast food joint/restaurant and restock.
4) Ignore all side missions and Optional Bosses, just focus on the main storyline and you should have no problem getting to the end with plenty of time to spare.
5) Right at the end of the game you will have the option of killing Gary or going to find Rhonda and bringing her back to him. Kill Gary, its far faster, less chance of dieing and is just generally easier. This Method means that you will NOT trigger overtime mode after completing Chapter 7 (you don't need to do overtime mode to obtain the achievement).
Killing Gary gives you an ending where you will not unlock everything, both achievement wise (Completing overtime mode) and in-game wise (New Gun). So if you want these things find Rhonda instead.
Hope these tips help anyone looking to obtain this achievement.
It really isn't too hard, following my tips above I completed the whole thing in under 4 hours and didn't die once.