OK, I wrote out a sort of guide to doing solo UW. I assume you know all areas of underworld and can do them quickly. This is more for ideas on how to achieve each area best with the same build, what order to do them in etc.
Soloing the Underworld
Build:
Elementalist/Assassin
Deadly Paradox
Shadow Form
Glyph of Lesser Energy
Ebon Battle Standard of Honour
Sliver Form
"By Ural's Hammer!"
Radiation Field
Death's Charge
Armor:
12 shadow arts, 12+1+3 earth magic, 3+1 energy storage
full aeromancer insignia, 2 attunement runes and superior vigor
Weapons:
sword, axe or spear with +20% enchantments and +5energy
shield with +10vs lightning and +30hp
earth staff with energy +5, energy +5 while enchanted, enchants +20%, customized
daggers with zealous, enchants +20%, energy +5
scythe with zealous, enchants +20%, energy +5
longbow with enchants +20%, energy +5
Candy:
essence, grail, armor - to perma, decrease damage, extra energy and movement speed
Candy corn, golden eggs - to perma and increase sliver damage and duration
Green, blue, red rock candies - speed boost and lower skill activation time
cupcakes, candy apples - for extra energy
pumpkin pies - for faster skill activation+attack speed when you do not want speed boost
ooze stone - to help in vale
essence, grail, armor, candy corn and eggs are up all the time. You do not want red/blue/green/cupcake up for donig 4h as they have speed boost. Vale is easier with cupcake and candy apple up the whole time.
Order:
1. Chamber
2. Mnts
3. Plains
4. Pits
5. 4H
6. Pools
7. Wrathful
8. Escort
9. Unwanted
10. Wastes
1. Chamber
Take clear the chamber, aggro all the graps and then pull them to behind the ghost benton so you don't have to kill aataxes.
Sliver the grasps, then run to lab and gather all aggro there
Pull along wall and kill the aataxes, grasps and terrors. Reaper can handle any nightmares, or a couple of grasps on low hp, but not both at the same time as nightmares strip his heal.
Take restore and unwanted. To kill keepers, use rad field and EBSoH then wand or dagger them. If the vengeful spawn far away you can sliver the first one on way to chamber, and you can always get a bit of sliver on the one at uw spawn. Kill these two then go to mnts.
2. Mnts
Take shortest path (obviously), sliver any behemoths you need to, kill terrors, take quest before he starts attacking. Kill slayer and 2 keepers then run to plains.
3. Plains
Run via pits side, making sure to aggro the wailing lords just north of monument area. Walk backwards/sideways if you have speed boost so wailing lords don't break, and walk along the north wall and they will break as you approach the pools side rider. They should end up in the right place to dcharge to for 4H. Kill the plains banished to spawn mindblades, and kill the patrol group. Pop reaper and then pull the 3 mindblades across to pools side and then north towards mnts and then across to pits side so they glitch. Run to pits.
4. Pits
Run to near reaper spawn, pull all enemies into a group at bottom of slope then dcharge in and kill. Pull the back group and terrors and use aggro to kill threshers at top of slope, then kill terrors and collectors and back group threshers. Take quest, hold aggro of terrors and kill the chained soul when it spawns if you were slow taking quest, make sure a collector does not spawn a minion from the body. Once spirits are at 2nd corner dcharge to chained soul at the top to break aggro, or run if it hasn't spawned (sometimes you may have to kill a terror or two). Tele plains.
5. 4H
Let SF run out then take quest, note you should not have a speed boost to do this (may be possible with a speed boost I'm not sure). Put SF up just before you reach pools side rider, then go aggro pools side horsemen and terrors. pull them along to where you will dcharge. Refresh SF and wait about 3 seconds then dcharge to wailing lords and run to catch pits side aggro. It doesn't matter if wailing lords aggro reaper as he will kill them easily, just make sure they make reaper move away from where you will pull aggro not towards. Pull pits side behind monument, catch pools side. Wait until all terrors are wanding you then sliver horsemen. Pull terrors into one group and kill them, reaper can handle the last few on low health. Run to pools.
6. Pools
Run straight to monument and kill terrors, again reaper can handle a few on low health. If you can take the quest quickly so reaper finishes of the terrors whilst you run to queen. Kill queen, go back to reaper and dcharge to spider to lose aggro then tele lab.
7. Wrathful
Kill the keeper on way, then run to vale and aggro all graspings and terrors, trigger cold group by going to statue and make sure you walk backwards so grasps don't break. Once you have aggro of the cold group, pull everything towards middle of vale so nothing is in aggro range of reaper. Sliver and rad field down the colds+terrors before all grasps die, then finish on grasps with reapers help if you like. Take wrathful and kill all but the top group on the hill with your summoning stone. Put up sf and aggro as many colds as you can then sliver the top group. DCharge to spider to break aggro and tele lab.
8. Escort
Take escort then tele vale. Run towards chamber and aggro everything, there should be 4 aataxes, 3 terrors and the mindblades. Use a longbow if needs be, just make sure you do not go too close to lab or lost souls will come to you. Block aataxes on stairs and sliver, then kill the minds+terrors. Lead the souls to mayor and tele lab.
9. Unwanted
Head towards wastes, killing the 2 keepers, and then you have to go slightly out of the way to kill the last one, you can sometimes sliver the last one if stuff breaks aggro, but the other 2 you have to wand. Run to wastes.
10. Wastes
Run to king spawn, aggro as many colds as you can and sliver any groups of smites near king, and then kill the 2 colds that are near king. Run to reaper spawn, losing as much aggro as you can then kill what is still on you and the terrors. Do quest, kill terrors and get your chest.
Challenge is to beat 54mins:
i dont like to tell secrets 
maybe you could drop gole again.
) somebody manages to beat 54min. I know 51 is possible using same tactics as I outlined here but with perfect spawns and no dilly-dallying, maybe 50 cos I'm kinda slow in wastes (Took me 5min in that run, and obv. it is possible to do in 4 with that build).