This is how I made it through Hardcore on Slender The Arrival.
First off DO NOT use Chapter Selection, it has to be done in 1 run. Of course you can pause but backing out to the main menu will cost you the Achievement.
*Having read some of the comments it appears it can be done in Chapter Select, I'm just speaking from personal experience. It didnt pop for me using stage select.*
Select Hardcore from the Options in the Menu and then Start New Game.
Prologue - This level can be blasted through by avoiding all collectables simply grab the flashlight from downstairs and run upstairs for the key open the door and then leave the house.
Run straight for Oakside and grab the collectable on the desk to end the chapter.
Eight Pages - Slender isnt that hard to avoid but make sure you conserve your flashlight by turning it off when your in a lit area.
You dont have to be super quick to find the 8 pages so take your time and if you see Slender go far around him.
Into The Abyss - Go straight for the Mine to conserve Stamina and here's the key to doing what for me is the hardest chapter on Hardcore GRAB THE GAS CANS FIRST, reason being is that you wont be attacked while your not touching the Generators.
Use your flashlight sparingly after turning on the first Generator and keep an eye out for the other Generators and try to remember where you saw them. By the time I'd grabbed the 6th Can I knew where all the Generators were and had plenty of flashlight left to survive to the Elevator. You can take maybe 2-3 hits before death.
Flashback - Easiest Level and no enemies.
Homestead - Just stick to the objectives and dont hang around any longer in the Cellar then you need, in other words grab the Gas Can and leave ASAP.
When you have the key make your way through the wooded cabin and cut diagonally right through the corn to the left of the rocks and aim for the gate.
Escape - Easy enough just avoid Slender while shutting doors and windows and if you see a warning sign telling you to hide bolt for your room shut the door and the level ends.
The Arrival - The only hard part of this Chapter is the forest fire. Its easy enough to avoid (unlike the P.C Version
) and if you see Slender give him wide birth which is easy enough just keep looking for the tower and run for it.
All in all this isnt the hardest Achievement but I would imagine most will struggle on Into The Abyss.