To start off you need the following:
A Conset to make your build work, which consists of a Grail of Might, Armor of Salvation, and Essence of Celerity which adds:
+1 to all attributes
+100 maximum Health
+10 maximum Energy
+10 armor
+1 Health regeneration
50% immunity to critical hits
damage reduction of 5
20% faster movement and attack speeds
20% reduction in skill activation
You will also need to bring two types of cons on your own:
Golden Eggs (+1 to all attributes)
Candy Corn (+1 to all attributes)
And I personally used for this run:
Candy Apples (+100 maximum Health, +10 maximum Energy)
Birthday Cupcakes (+100 maximum Health, +10 maximum Energy, 25% movement increase)
Red, Blue, Green Rock Candies (only for Mountains/Pools portion)
Okay! To start off, Clearing to Chamber and the actual chamber itself!

After getting quest I Death's Charge up to an Aataxe and precede to aggroing all the Graspings.


Then I solo block them just up the main set of stairs in entrance room and kill using Radiation Field and Light of Deldrimor


Next I aggro all of chambers and pull them all in range of Radiation Field while right wall blocking Aataxes/Graspings

Next I get Unwanted Guests and Restore Grenth's Monuments and head to vale to clear the keeper/terrorwebs that popped up. Also I had to kill the 2 Aataxe patrols in that area.


Again right wall blocking the Aataxes so they can't flee from degen

Next I gathered up all the graspings in vale and pulled them behind the house to prevent scattering then Radiation Field/Light of Deldrimored them dead.



Then I aggroed the Coldfire patrols and Terrorwebs and pulled them into the standard position to be killed during vale clear. After Reaper was spawned I teleported back to Chamber to finish off Unwanted


Next I ran up the Mountains towards Mountain shrine/Reaper


As you can see there is a 4 stack of behemoths so I killed off the 2 extras to provide myself room then i proceeded to getting a Healing Spring rotation down to wand them in a certain order and Radiation Field/Light of Deldrimor them down. (If any cast Healing Spring during my other spells, "You Move Like a Dwarf" is PERFECT for interuptting)


After Reaper was spawned I got quest and headed down to tank Slayer.



After Slayer is dead I killed the 4 Keepers for ecto chances (soloing UW is costly!) and I did luck out


Next I headed to Pools while my Red Rock Candy was still fresh.




After gathering and Radiation Fielding the Terrorwebs I grabbed pools quest and set off to kill her.


Notice how I pulled the extra Terrorwebs to get 3 targets for my Zealous Scythe to keep up the energy to chain "You Move Like a Dwarf" and Holy Strike.
Next I was off to Pits, a my UW home for the past year!




At this point I was 5/10 done with UW. Left was Escort, Wrathful, Servants of Grenth, Restore, and 4 Horseman. I decided to attack Wrathful head on, however with little preparation and planning that failed

Feel free to comment. Hold the "you are wasting money" or "sins are faster" comments please. I did this as a self achievement sort of thing and just wished to share with other that Monk perma is STILL alive and doable. And to try and think outside the box a little.
My Monk Perma Builds:
Pits:
Special Equipment:
A Zealous Scythe of Enchanting can be helpful at times, but I have never required one.
Attributes:
Smiting Prayers:12+1+3+3=19
Shadow Arts:12+3=15
Deadly Arts:3+3=6
The Rest:3(Golden Egg, Candy Corn, Grail)
Skills:
Deadly Paradox
Shadow Form(E)
Castigation Signet
Symbol of Wrath
Kirin Wrath
Radiation Field
Light of Deldrimor
Death's Charge
Pools:
Attributes:
Smiting Prayers:12+1+3+3=19
Shadow Arts:12+3=15
Deadly Arts:3+3=6
The Rest:3(Golden Egg, Candy Corn, Grail)
Skills:
Deadly Paradox
Shadow Form(E)
Castigation Signet
Holy Strike
"You Move Like a Dwarf"
Ebon Vanguard Sniper Support
Radiation Field
Death's Charge
For Pools I Always use Rock Candies to run faster through the Sludge. I suggest you do the same, otherwise you will find the lack of IAU difficult.
Chambers:
Attributes:
Smiting Prayers:12+1+3+3=19
Shadow Arts:12+3=15
Deadly Arts:3+3=6
The Rest:3(Golden Egg, Candy Corn, Grail)
Skills:
Deadly Paradox
Shadow Form(E)
Castigation Signet
Holy Strike
"You Move Like a Dwarf"
Light of Deldrimor
Radiation Field
Death's Charge
For Chambers this build is used to clear Chamber then spike each keeper.
Mountains:
Attributes:
Smiting Prayers:12+1+3+3=19
Shadow Arts:12+3=15
Deadly Arts:3+3=6
The Rest:3(Golden Egg, Candy Corn, Grail)
Skills:
Deadly Paradox
Shadow Form(E)
Castigation Signet
Spear of Light
"You Move Like a Dwarf"
Light of Deldrimor
Radiation Field
Death's Charge
For Mountains I use Rock Candies for faster wanding to interupt the Behemoth's Healing Springs.
(There is a faster variant for monk mnts, but it is not my build to share here
