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Beat the game on Blackest Friday difficulty.

These do stack, so if you want to go that route you can. That said, I'd recommend being at a high level before starting this (I was somewhere in the 80s).

Some general tips/things to note:

Keep moving. Avoid combat when you can. If surrounded by a big crowd, just clear out enough zombies to be able to keep moving.
Don't bother with the maniac side-missions.
You take way more damage than you do on normal. Likewise, health items restore way less health (150 health once you have all the health-related perks). Some bosses/exo suit troops can kill you in a couple of hits if you get too close, so keep your distance.
Weapons break way faster, and guns generally only hold about a quarter of the ammo that they do on normal. However, for some reason, the amount of grenades you can hold wasn't nerfed.
On a related note, Gold weapons (especially ice swords and roto killers) are highly recommended, since they're stronger and last longer than regular ones. Unlocking them requires playing multiplayer, however (see "Workin' Hard" for more info).
As noted on "Hunting Grounds," your found locations will reset when you start a new game. Almost nothing else will, however - your level, perks, safe rooms, collectibles, blueprints, even panic room keys will all carry over (well, most of your panic room keys - the one on Tom's farm doesn't).
It's good to carry multiple Split Shots at all times to deal with crowds, as well as melee weapons that can quickly clear a path for you (the Gold Roto Killer is a good one for this)
While the game is definitely harder, it's not impossible, particularly if you start leveled up.