Since enabling hard mode might not be common knowledge, here is how to find the hard hat.
Firstly: Don't skip the Prologue at boring springs.
Secondly: Find a shiny rock at the Thousand Snakes Gulch location and the two bits of Ore at the Orehole Mine and sell them to Crazy Pete at the Saloon in Boring Springs.
He'll remark about something very scary hidden on the 40th floor of the Orehole Mine's Elevator,
something you want to avoid if you're attached to things like your eyeballs.
Since you want to beat hard mode in one ingame day, I'll assume you're not too attached, so just go for it and ignore all the warnings.


-The stats of all enemies will be higher than in normal mode.
-Silver-plating the Turnip will cost 20k Meat instead of 5k. Various other things will be more expensive too.
-You may not take Gary or the Dark Horse with you, as a result some random encounters will be entirely unavoidable.
-You may never take off the hard hat, meaning you have to go without any stat boosts from your Hat.
This also means you have to plan carefully which snake's hide you wish to use as a hatband.
Further, this means in certain locations you may not gain access to specific perks or dialogue options,
for example to achieve the Kurtzian Physique perk you're required to wear both the Kurtzfit Pants and the Kurtzfit headband, but since you may not wear the headband you can't gain the perk.
Also perks or quests requiring you to sleep are out of the question and you may not get any packages from Rufus.
-In certain farming locations, the hat will stop you from farming EXP for "the rest of the day.",
preventing you from simply farming.

In order to finish the game easily, you need to acquire three things:

1) A Year's Supply of Dynamite.
2) A Bridge
and
3) A way past Norton at Frisco.

There are various ways to achieve each of these goals, truth be told, but a few of them are simply easier to achieve than others.


How you get the Dynamite is not important, here are some ways to get it:
-Saving 8K Meat and buying it.
-Getting the Coupon from Barnaby Bob
-Retrieving it from Gustavson's Gulch.
All these methods will work and how you achieve this part is up to you.


There are 3 Bridges.
The bridge I'd recommend is the Bone Bridge,
as it's the easiest of the bunch. All others require a lot of travelling and/or fighting,
which in hard mode translates to fighting and/or fighting. And you want to avoid such.
If you want to spend more time feel free to get any other bridge, but this is the fastest, easiest way.


You could always go on a mad train chase, sure, but it's easiest to give a Crown to Norton.
You could save up 20k for the Turnip Crown or somehow go through the whole El Vibrato questline to get that crown, but the way I'd recommend is the gold tooth crown.
Note: This is DIFFERENT to the gold tooth tiara.
The tiara only requires 10 golden teeth while the crown option only shows up at roughly 25 golden teeth.

Note: From here I'll assume you've played and beaten the game at least once before.
If you don't recognize an item or place, just explore.

From the Menu start a new game and select the Snake Oiler as your class.
When you receive your first skill book, make sure to pick Lockpicking.
Here's why: As you only play a single day, you'll have few methods to actually farm XP.
You'll want Lockpicking maxed out, and the Snake Oiler just so happens to only need half the XP to level it up. I recommend going with Susie, as she has powerful single-target damage and will get a stun later on. I also recommend using the ghost horse.

From there on out, you're free to do what you want and level up the stats you wish.
It's still recommended that you level up Lockpicking early, as well as Grit, as this will give you a few "free losses". Since you only have a single day, make sure not to "waste" any of your Spleen, Stomach or Liver Slots.

I used 3 Ranch Dressing as my spleen items and had I gotten the Big Spleen skill from a Magazine, I could've doubled that amount. More HP improve your chances to win.
Also, you want to strive for having a stomach stat of 4, but make sure to eat the ghost pickles first.
These two things alone will drastically improve your survivability in the starting area.
Once you reach the old medicine show, max out your snake oiler crafting skill and create some of the following:

- Liver + Spleen + Venom => Pure Snake Spirits, Liver Item with +9 to all Base stats.
- Venom Gland + Liver + Venom => Patent Vitality Serum, Spleen Item with +7 to all Base stats.

I'd recommend at least filling all your liver points with Pure Snake spirits and going with the vitality serum or the Ranch dressing depending on how you need it.
As your fourth stomach item, the beaker of Fudge is definitely recommended,
but make sure to get the Buffalo Animating Fluid first to avoid any of the tanks clogging up.

As you're limited to the hard hat, make sure to pick your snake skin wisely. The Coal Snake Skin comes to mind as, as a snake oiler, Moxie will be your main stat, but there are two others I can also recommend:
-Sick Python skin (+30 Max HP)
-Frisco Viper skin (+3 to all stats, can be gotten early on and without a fight from a random encounter if you have a varmint skinning knife on you and use it to deal with the encounter)

That's about it.

To get the Bone Bridge you need 4 Necromancer Tomes and Lockpicking maxed out.
Visit the Buffalo Pile and open all the lockers, you'll find the Buffalo Soldier Diagram in one of them and you can hide in the closet to find out the recipe for the buffalo reanimating fluid (or if you're too lazy or already know it, it's Milk, Blood, Ichor.). Afterwards go for Milk, Milk, Lemonade to get the Beaker of Fudge which comes with a tremendous stat boost.
Get the Bones from the shelves and summon Buffalo Buffalo Buffalo Bill, let him join you and kill the cultists. This gives you unlimited bones.
Then you can go to the Railroad Camp at any time, read 4 Necromancer Tomes and summon a Bone Bridge to the next part.

To get enough Golden Teeth, ask the Bone lady at the fort of darkness for a Bone Chip Ring, then return to dirtwater, wear it and simply wander and farm easy skeleton encounters until you have enough teeth. Return to her, get the golden tooth crown, then travel to Frisco, give it to Nortan and you're done. That's all there is to it.

That's the basic structure of what you want to do. Now on to a few further tips to make it easier.

Once you got the Ranch Dressing, the Ghost Pickles and a few Stat Boosts from your other equipment, you should be able to survive anything in the first area of the game. You don't need to go to areas like Danny's Tannery or to the thee bosses of the Catacombs of the Old mission,
but try purchasing all the dynamite you can find or use extra year's supplies of dynamite to get a lot of the stuff. Dynamite is a nice combat item, it deals 20 Damage regardless of stats and it doesn't end your turn, meaning if you get the first strike you can cheese late-game battles by simply spamming dynamite. This also makes the Quick draw perk the snake oiler has a good idea.

Don't go into the middle area unless you have one less Angry "buff" than your pain tolerance stat. Chances are you want to invest some points into hornswogglin' to avoid fights more efficiently.
Also, all El Vibrato Encounters can be avoided, meaning if you get the el Vibrato device from the Humming Cave you can decrease the likelihood of unavoidable fights.A good strategy is avoiding as many multi-target battles as possible. Susie can stun a target for one round after a while, and Fanning the Hammer can deal a lot of damage too. Just make sure you get good equipment,
such as the befouled pistol, and make sure to get a lot of stat increases from your other equipment,
e.g. the extra large boots, Kurtzfit Pants, etc. and make sure to Silver Plate all your equipment too! It's a small but quite important boost.