There are three ways to unlock the Trials of the Foolhardy.

The first involves a long intensive process that is inaccessible to those who can't find 3 other people to commit hours to unlocking it legitimately.
The second is to wait (and hope) for a publicly hosted map in the Lobby Browser.

And the third is to mod the game.

To unlock the elusive level, you can download the "Unlock Trials of the Foolhardy, without 4 players" Mod from this REDDIT THREAD and follow the instructions for installation.

This mod will change the Random Map selection button on the main map to ALWAYS choose the Trials of the Foolhardy mission even if you haven't unlocked it yet. Upon completion of this mission (on any difficulty) you will unlock the level permanently and you can delete the mod to return the Random Map button to its original function.

To install make sure to extract the trialsOfTheFoolhardy.LUA file and copy it into the following file path:
steamapps\common\Warhammer End Times Vermintide\binaries\mods\patch

**NOTE: You will need to have the Quality of Life V15 modpack installed for this to work. You can find out how to install this mod pack here:
https://steamproxy.net/sharedfiles/filedetails/?id=1090355288

When you start the level you'll be met with a lever and a closed gate.
This lever will open portals spread throughout the map for a limited time. You have approximately 30-45 seconds to get everyone through a portal... as anyone caught on the other side after it closes will be stranded from the group.
When you hear a voice line from the Wizard, it marks you have approximately 7 seconds before the portal finally closes. Worry not! After a waiting period of approx. 10 seconds, the levers will become highlighted to indicate you can reactivate the portals thus allowing free traversal.

There are FOUR portals spread around the map in static locations.

The Snow Portal:

The Forest Portal:

The M.C. Escher Portal:

The Town Portal:

You'll generally have enough time to reach the next portal after exiting the previous portal. If you are unable to reach the next portal in time; you'll have to repeat the process with the first lever on the ground floor and bunny-hop your way to the desired location, periodically taking refuge in the portals leading up to your destination.

You don't need to complete the objectives inside any portals to be able to exit the level that portal contains. 👍

The objective of this level to find three keys inside highlighted crates scattered across the map. You will only need to open the crates for a key to be 'found'.

Upon finding all three keys, TWO Rat Ogres will spawn and you will need to make them PERISH in order to collect the relic. This is the real trial of this level. It is highly recommended that you stock up on any ammunition and health potions available for this fight.

With the Rat Ogres dead you can collect the first ingredient: chip of Urszebya stone

The objective of this level is to break the three magic seals in order to open the relic's tomb. To break the seals, just hit them really hard with your melee weapon a few times.
An easy way to figure out the locations of these seals is to use the bridge construct in the centre of the map as a landmark, facing NORTH in the direction of how you first entered the map.

When exiting the portal, turn left and head up the hill to reach the first seal. South-west of the bridge.
Cross the bridge and turn right to head towards the second seal. North-east of the bridge.
From this point, head to the location of the relic in the tomb. Facing the tomb, turn left to see this path heading upwards and take a hard left around the rock formation. The last seal will be hiding behind some low hanging tree foliage. North-west of the bridge.

Now will all three seals broken you can collect the second ingredient: the Bone Relic

Upon landing in this room, it might be confusing at first but fear not, the steps stay the same each time. First make your way to the Ground Floor, initially avoiding the pits. You'll want to find this particular pit first and jump through the sideways door.
Go straight down the hall and turn right to enter the portal behind the ladder.
You'll be spat out somewhere high up so try not to fall. You'll want to skip along the top of the bookshelves and enter through the sideways door.
Go through the portal in the corner.
From here, pass through a sideways door AGAIN and make your way up the ladder. Go straight to the end of the railing platform. You'll be needing to jump down from this point.
Aim for this platform when jumping. Best method is to jump fully towards the wall blocking your jump arc and falling forward from there. Turn left upon landing.
Head through the upside-down door and through the portal shown in the picture.
This is the tricky part. You'll find yourself on a platform and your destination is the balcony below around the corner. To easily get there, crouch and hug the wall while pushing onwards. No jumping required. Once on the balcony, turn to face the upside-down door...
...as shown here. Go through the final portal to behold...

You can collect the third ingredient: the Crystal Prism

Now to head back to the home portal... turn around and go through the portal you just exited.
From here you can simply drop down onto the next balcony below, and follow the path right back to the start~!

Now you're thinking with portals... haha...

The trial for this level will test your ability to navigate the area in darkness to light candles in three places around town.

When arriving to this level, you will be in daylight and therefore will have a chance to explore the town before the next stage. Take as long as you like to familiarise yourself with the layout of the town. In particular, you'll want to know how to navigate around using the Church as an anchor point.

The three locations you'll want to know how to get to include:
The Alley, the Picnic Tables, and the Ship

Keep these locations in mind when it comes to phase two.

Now return to the Church. Inside you'll find a chest containing the last ingredient you need for the Wizard. Note: OPENING THE CHEST WILL PLUNGE YOU INTO DARKNESS !!
Opening the chest will reveal...
...an even smaller chest! How cheeky!

You'll now be prompted to go light the candles around the town. Turn around and next to the doorway is a torch to help you get around in the dark easier.

When exiting the church take a hard right towards the Alley. You'll run into a well that can help you know when to take another right into the Alley.

Next to the cloth-covered barrels, you'll see a floating black cloud waiting for you to press E on it. These clouds will be how you can spot where the candles must be placed.

After lighting the candles in the alley; turn around to face the stairs and follow the path towards the picnic tables. Passing by the fountain means you're on the correct path. Just keep going straight.

In the Picnic Table area, turn left to look around the corner for a bench and you'll find the candle spot in front of it.

From this point you'll want to head towards the Ship. Aboard is the final spot for the candles.

Time to head back to the Church... while crossing the pier back to the street, you'll take a left towards the arches. Through the arches you can see the lights of the Church.

With all the candles placed, you can collect the forth ingredient: the Eyes of the Newt

For the next 5-10 minutes you'll be fighting the ravenous hordes while the Wizard performs the ritual. Find a defensive spot and group up. The area behind the bookcase where the Escher Portal is located is a prime spot for defence. Choke points will prove invaluable in this fight.

When time is up, the objective will pop up again onscreen to let you know the section is over. The Victory screen will soon follow and depending on the difficulty you can gain the following achievements:

An incredibly gracious thank you to JBles95 who made the mod to Unlock Trials of the Foolhardy. Without this mod I would have been eternally locked out and never would have gotten to experience this free DLC level.

I'd also like to thank Nocturnal Pie for their guide on how to unlock the Trials as well as it helped me through the initial stages.
https://steamproxy.net/sharedfiles/filedetails/?id=973128579
Another thank you to Onihikage and Polikua who helped me with unlocking the Trials as well. I never would have gotten as far as I did without their help.

I wish you the best of luck with passing the trials and getting the achievements. Feel free to leave a like and a comment if this guide has helped you~!