Hi!
You will need to beat the game once to be able to play Classic Mode in a New Game. Classic Mode is Nightmare Difficulty (the previous hardest difficulty) with the removal of autosaves and the ability to upgrade your weapons or skills.
You're given 7 manual saves to use through your game in any of the normal spots. Here is where I used mine:
1 - After the gas room, before City Hall (end of Chapter 4)
2 - After dodging the light, just before the Stefano boss fight (halfway through Chapter 8)
3 - After completing the wheel puzzle but before the shootout with Torres (end of Chapter 9)
4 - After fighting with O'Neal but before having Torres blow up the Emitter (end of Chapter 11)
5 - After reaching the hotel (a mirror will appear when you tell Hoffman you are not yet ready for the fire escort near the end of Chapter 13)
6 - At the elevator just before the Theodore bosses (end of Chapter 14)
7 - In Sebastian's room before Myra (Chapter 16)
Here are some tips you might keep in mind when going for this achievement:
-Most bosses will give you an infinite supply of ammo to kill them with if you run out of handgun ammo
-A lot of locker keys are easy to access and will give you a good amount of materials to use
-The shooting gallery will give you a large amount of materials to use for free
-Using a Medical Syringe replenishes some stamina as well which is useful when you are being chased
-Bottles can be very handy for bypassing a group of enemies and you'll find them everywhere
-Stomping an enemy makes you invulnerable for a moment and will always kill them instantly
-Take advantage of stealth kills to save materials and get easy instant kills
-The hand axe will often kill basic enemies in its one swing
-You cannot upgrade your weapons but you CAN loot ammo pouch upgrades
-The crossbow bolts are all very useful, I suggest getting a feel for what they all can do because even in their basic forms they can allow you to instant kill enemies or distract a room you're having trouble with
Finally, if a visual example is more for you, I have made a video of a Classic Mode run with some commentary below:
I'm very open to feedback if you have suggestions on improving this guide so please let me know :)
Good Luck!