I haven't done it, but just general obvious advice:

Have a few friends you can call on to take hits for you if need be.
Avoid continuing in arena, sure the second round may be easier than the first, but you didnt' come for money, you came for an achievement.

Choose a gate with stuff you can actually beat easily, mainly in the end for tier 3. Better to avoid boss stratums. Snarbolax is sorta ok if you want to go there. Roarmulus is easy enough for me so you might want to consider that one (I tend to die at least once in JK I don't know about you =T).

And maybe wait around for preferred clockworks stages. Like if you're in a shock strata, perhaps it would be better for you to wait for a Devilish Drugery to pass in favor of Wolver Dens (or vice versa if you're better at the opposite).

Ok, here we go.

For equipment:
Any sword with a sufficient amount of knock back (leviathan etc etc), as for a secondary weapon bring a gun (Polaris or Argent Peacemaker). There will be plenty of opportunities for you to shoot around corners and kill things that might otherwise give you more trouble than they're worth. Retrodes/Giant Toxilargoes etc etc.

Switch your Armor/Shield to whatever defense you have that will be optimized for the floors below, that's just common sense however. Changing for the stratums will make it much much easier.

For consumables:
Personally it would be a good idea while playing solo to grab hold of any and all pills. Generally using the ones from your current tier and the ones from the previous one. T1 pills in t3 is a little silly but if you're feeling particularly paranoid I'd pack them as well. Use the pills for your current tier. The ones from previous floors are only in case of an emergency or if you're just particularly unlucky with health drops.

Remedy. I don't care what anyone says, if you're attempting to solo this (it's easier in some ways due to health scaling) then grab a remedy. Nothing is worse than being chain shocked to death and having the effect reapplied upon every subsequent hit. If you feel comfortable with only 2 sets of pills I would go with Gwen's recommendation of stun vials. A little bit of knock back, some breathing room and they would be stunned. Making for an easier getaway.

That's it from me. Every other player touched on the important details.

1) Have a variety of gear so that you can use a shield, helmet, and armor that protects well against the mobs in each stratum. Four star gear that is appropriate to the stratum is fine. Five star gear with only normal and elemental defense is not fine in a stratum where mobs mostly do shadow damage.

2) Get some skills. Do tier 3 for a while until you can often get gold survivor without particularly trying for it. Don't try for dauntless delver until you can do this.

3) Pick a gate that involves neither jelly king nor vanaduke for your attempt. Those two fights are too random, and can get you killed even if you're good. Snarbolax and Roarmulus are far more dependent on player skill, so you should be able to reliably beat those without dying.

4) Skip danger rooms starting in the fourth stratum, and third arenas starting in tier 3.

5) Save your health capsules from earlier tiers until you need them. If you have three tier 1 health capsules and three tier 2 health capsules at the start of tier 3, you can save them until you run out of tier 3 health capsules and need some more health to bail you out of a bad situation. If you can't finish tier 2 with a full complement of health capsules, then you're not good enough to do dauntless delver.

6) Pick a time when you're sure to have a few hours uninterrupted. If there has been a patch earlier that day, there is likely to be another, and that will spoil your run.

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I did dauntless delver in mostly four star gear. My only five star gear was a trinket, and my other trinket slot was empty. I also did it in a PUG, though a couple of people from my friends list jumped into the group for part of the way.

Don't die.

Very important to note. See those health capsules on the ground, but you're already full? Take them with you anyway.
It will result in a lot of backtracking to fetch capsules from all over the place, but if you screw yourself over they are good insurance.

For instance, just before writing this post I decided to go for Dauntless Delver - and succeeded. However, I got in a pretty tight spot in Tier 3, facing off with a vilewood and a bunch of isotrodes in a crammed room, that kept sniping me with their beams as I tried to pick out the vilewood. Having those health capsules around that I dragged with me across the level, I could heal myself without feeling guilty about spending a health capsule, as I could replace it instantly by picking it up right by me. Even if you're feeling confident about your skills, like I said, they're good insurance. If you do screw up, it's good to have 'em around, even if it takes slightly longer to finish the level. The goal is, after all, to get through alive.

First, you need the right gear.

This will work.

Divine Veil+Skolver Coat+Fire Resist UV on the Coat (If fire in T3)
OR
Vog Cap+Radiant Silvermail

(Mainly for sword only users)

Shields-You want the most Ot can cover first, then throw in some UVs.

A CoA with high ele+ is good, a grey Owlite with shadow high+ is better, and then I hope you got yourself a Barb Thotn Shield.

Weapons-

For a all swordie who WON'T use Vog set (One piece is fine, but not recommened)

Acheron
Divine Avenger
Barbarous Thorn Blade
Supernova

Trinkets-Elite Slash Module x2

For a gunner-

Polaris
Blitz Needle or the (BLEIGH!) Magnus Line.
A Umbra Driver (Recommended) or a Biohazard
Leviathan Blade

For a bomber-

Nitronome
Radiant Sun Shards OR/AND Dark Briar Barrage
(Here, I really don't know. The next weapons)
Either a Supernova or Leviathan Blade
Whichever you didn't chose, the DBB or RSS goes here.

Gear for bomber-Trust me, you won't regret it.

Volcanic Demo Helm with shadow AND/OR piercing uv high+
Mad Bomber Suit with shadow high+ AND/OR piercing high+. (No need for the fire uv, your not gonna be in FSC anyway)

Trinkets-

Elite Boom Focus x2

In the en for a bomber, MAX CTR at heat 10, MAX Damage boost, blah blah blah.

Time-Running through every level takes about 3 hours or so, maybe a little more.
Fightin them is about 4-5 hours.

I would get some bombs and a piece of volcanic demo for T3.

Freeze bombs will effectively put a halt to everything except wolvers in T3, who do that dig/teleport thing. Firebombs are dream kiting material. Volt bombs are the same, but a little less effective. Blast bombs...I dunno. I would stick with the beer cans if you aren't going to go full-bomber.

Bombs 1) don't activate the dodge reflex, 2) hardly ever miss, 3) keep you enemies far far behind you, and taking damage. The average damage my bombs do on ignition is on par with a sword swing, elemental. When kiting a room, you're bound to hit a few mobs with that.

I was a total striker before, and although you can really lay on the damage, you're in range for being attacked. Survivability really drops when they have a chance to hit you. Personally, all the JK levels (except JK himself), any of the old danger rooms, and most arena battles aren't able to hit me as I run around and around, dropping status bombs behind me. It's boring, but coming out of the JK levels with more HP than you started is a good signifier of power.

I would suggest your favorite sword, a good gun, and 2 status bombs. I would either pick a freeze/fire, or freeze/volt, depending on what's upcoming in the level. I have my CIV, Polaris, and whichever bomb.

If you decide on a blast bomb, it appears like they're a good choice from FSC, due to the knockback. If you can get a CTR blast bomb, convert it to a nitro and create a murderous haze of explosions around you, making you untouchable to non-shooters.