In order to gain access to madhouse difficulty, you must clear the game at least once on easy or normal (unless you have the Survival Pack: Recovery Set pre-order bonus, in which case you can play madhouse right away).

Madhouse has many differences compared to easy and normal:

You need cassette tapes in order to manually save the game. Cassette tapes can mostly be acquired in save rooms by cassette recorders.
There are almost no checkpoints
Enemies are twice as fast, detect you much faster, do more damage to you, and take more damage from you.
Item placements from easy/normal have been rearranged, and items are rarer to come by.
There are thirty-three antique coins to collect on madhouse, compared to the eighteen on easy/normal.
Madhouse encourages some stealth, item crafting, and item management more than easy/normal. Avoid combat whenever you can. Save ammo for the boss battles and try to sneak or run past common molded enemies.

If you've already cleared the game at least once before you started madhouse difficulty, you will gain access to the Albert 01-R once you arrive at the main house. If you've finished your speedrun playthrough, you'll have access to the circular saw which makes madhouse significantly easier. Both weapons will be very useful on madhouse, especially during the boss battles in the morgue, greenhouse, barn, and boat house.

Another useful weapon is the broken shotgun, once you repair it into the M21 shotgun. On madhouse difficulty, spend three antique coins to acquire the scorpion key from the bird cage in the main hall. Use the scorpion key on the door upstairs in the recreation room to get the broken shotgun. You can find a repair kit once you step outside into the yard. When you walk down the steps from the dog head door, immediately walk to the right, then turn right again into the shrubs/bushes. A repair kit will be tucked away here on madhouse difficulty. Combine the repair kit with the broken shotgun to have a functioning M21 shotgun.

Make the branching decision to earn ending 1 when you play on madhouse in order to avoid a boss fight. It's a small fight that isn't all that challenging, but in case people have trouble with melee battles just remember to get ending 1 in this playthrough.

Boss Notes:
Mia (Guest House - First Floor):
There's nothing much to this fight, other than alternating between attacking and blocking. Pick up the axe. When she's getting ready to swipe at you, block, immediately attack her afterwards, then block again. Continue to do this until she goes down. MAKE SURE YOU PICK UP THE AXE AFTER THE FIGHT. If you can't find the axe immediately after beating Mia here, wait for the call from Zoe. After the call, return to the room and the axe should be on the ground.

Mia (Guest House - Attic):
This is the toughest fight on madhouse difficulty. If you can beat Mia in the attic, you can beat the game on madhouse. Make sure you have the axe with you (from the previous fight) before you enter the attic. Look around the attic for handgun ammo. You should have 27 bullets. Make a save at the cassette recorder on the second floor behind the attic stairs before starting the boss battle.

Always aim for Mia's head, and try to not miss a shot. She can break down all three doors in the attic as well as the center wall, so use that to your advantage. Shoot her head right when she finishes her animation after chainsawing the doors/wall.

Run in circles around the attic, turn around, and keep shooting her in the head while she walks toward you. If she runs at you, then run back in a circle around the attic again.

If you run out of bullets and she hasn't gone down, you'll have to resort to the axe. Try to block her attacks while you still can (you can't keep blocking them forever as you'll gradually lose health), and hit her with the axe in between her chainsaw swings.

Jack Baker (Main House - Garage):
Don't bother wasting ammo. When Jack attacks the Deputy, run to the back left corner of the garage where the yellow shelf/table is. Pick up the lockpick on the table. Run to the lockbox in the opposite corner of the garage, use the lockpick on the lockbox, and take out the car keys. Get in the car and start it up, then proceed to run over Jack with the car.

Later on, when Jack is on fire and exits the car, keep your distance and don't let him grab you to avoid extra damage. The car should explode very soon, which will knock both of you down. Exit the garage via the ladder by the table with the lockbox where you took the car keys. If the game won't let you climb up the ladder, make sure you pick up the Deputy's handgun that was dropped on the floor, then try climbing up the ladder again.

Jack Baker (Main House - Morgue):
Bring the circular saw and the Albert 01-R to this fight. Avoid Jack's axe until the axe breaks. After he grabs his makeshift chainsaw/scissor weapon, start shooting with the Albert. Once he mutates a little bit, cut him with the circular saw when he's kneeling on the floor. Shoot him with the Albert when he stands back up, then use the saw when he kneels again.

Marguerite (Old House):
This is when Marguerite throws you from the crow door and you fall into the pit. Shoot her with the Albert and M21 shotgun for a little. If any bugs appear, take them down with the burner. You can also deal some damage to Marguerite with the burner. When Marguerite falls into the pit, immediately climb back up the ladder.

Marguerite (Greenhouse):
Make a save before entering the greenhouse. Bring the Albert, the M21 shotgun, the burner, and the circular saw.

When you walk up the stairs, be careful of Marguerite once she bursts through the window. You can avoid her grab attack by stepping back down the steps or quick turning and running back down. Shoot her in the head to get a couple of free hits before she leaves the window.

Aim for Marguerite's weak spot underneath her belly. Rush in and use the circular saw to deal big damage when you can. Aside from that, there's not much else to this fight other than paying attention when she runs away and creates an insect nest. When you hear her heaving and groaning, follow her sounds to quickly find her and attack before she lays a nest. If you took too long to find Marguerite, that's ok. Just use the burner to get rid of the nest.

Double Bloater Testing Area Fight (Barn):
When you get to the end of the testing area, the last fight you have will be against two of the big bloater enemies that shoot vomit and bile at you.

Hide behind the bales of hay. Use the M21 shotgun and enhanced handgun ammo for the Albert and pull off headshots on both of the bloaters. When the bloaters go down, stay back since they explode and can do damage upon death if you're close enough.

Mutated Jack Baker (Boat House):
Stock up on health items, bring the grenade launcher with flame rounds and neuro rounds, enhanced handgun ammo for the Albert, the M21 shotgun, and the circular saw. Hop down to the bottom floor, and shoot the eyes hiding underneath Jack. Shoot him with a neuro round from the grenade launcher to slow him down, and take out some of his eyes with the circular saw. Keep alternating between the floors and run to the corners for different vantage points. Try to break all of the boxes with the saw in order to find more ammo and health items.

After taking out all of Jack's eyes, he'll go underwater then reappear with a new eye on his head. At this stage, block his attacks and shoot his last eye when he's readying up for this next attack. Keep alternating between blocking and shooting until he goes down.

Mia (Ship):
This boss battle only happens if you cure Zoe with the serum for ending 2. You can avoid this fight entirely by curing Mia with the serum.

If you fight Mia here on madhouse anyway, this fight is basically the same as the first time you fought her in the guest house. Walk behind you and grab the crowbar on the ground. Equip the crowbar, block Mia's attack, then hit her with the crowbar. Alternate between blocking and attacking until she falls.

Double Bloater Fight (End of the Mines):
Here's another double boater molded battle like the one in the barn. However, you can skip this one if you save some remote bombs and neuro rounds for the grenade launcher.

Shoot the three trip mines on the ladder leading up to the guest house. Use the remote bombs to stun the bloaters and knock them down. Shoot them with neuro rounds from the grenade launcher so they'll move slowly for a couple of seconds. Run up to the ladder and climb before one of the bloaters can recover and knock you down from the ladder with their vomit.

Final Boss (Return to the Guest House):
This fight is relatively simple and plays out the same as it does on the other difficulties. It's certainly a nice and relaxing fight compared to most other bosses in the game!

During the initial phase, block her shockwave blasts and run to her in between the blasts.

For the next phase, shoot her face with the machine gun or Albert until you're thrown out of the guest house.

In the final phase, just keep shooting at her with the machine gun or Albert until she drops you on the ground. Grab the Albert 01 that was thrown from the helicopter and fire away at her face.