Here's a step-by-step guide to SpeedRunning. SpeedRuns are slightly different than what you remember of doing it the first time, when you don't know what's going on. But once you get down to it, there are many shortcuts that can be used, and this is what I'll touch here.
First Part to Reaper boss
Only pull the 4 Soldiers in front of the lights. Avoid the ones on the right side, and don't get close to the area in the middle.
Once the two searchlights are off, sneak along the left side, its possible to avoid most of the monsters on the road, save for the hound and two guards at the end of it.
Tank Reaper boss near one of the two side doors so you can pickup adds as they appear, off-tank the ones from the other door easily.
Second Part - After Disposal Chute
Sneak along the right side wall, you can avoid the first reaper as long as its not too close to the bump in the wall there.
Kill the monsters near the searchlight and turn it off afterwards.
Sneak along the right wall again, you can walk behind the two guards in front of the gate if you hug the wall closely.
Kill the guards in front of the refinery, you can pull them on the refinery to avoid the wandering reaper behind you.
Its possible to sneak past some of the guards to put the explosives too, the reapers sometimes are looking away. Its wroth the attempt at the very least.
During the Vanguard boss, tank near the right side door to pick up adds. Healers should be standing near that door too, so the other adds need to cross the entire area to get to them. Don't kill the reaper when it appears, only off-tank it and finish the boss fast instead, but kill every other small adds. Sleeping them helps too, especially archers and casters.
Third Part - Escorting Cid
Cid can destroy the first group there, but lots of people just pull them straight to the cannons ahead. Make sure you stay away from the cannons, especially the tanks, so they don't get overly hit and destroyed prematurely. You want to keep those cannons.
After the first group, there's a single Signifier in front of the search light, which will dismiss a good part of the path there. And then pull the vanguard patrolling nearby to the cannons again.
The group in front of the Phantom Train station can be ignored, sneak on the left to the next part, grab the Vanguards and turn the cannons on them. These don't need to be preserved, but if the first batch got destroyed you can use these right after the boss.
During the boss, there are no special tricks than handling lots of adds and tanking the boss on the incline.
Fourth Part - More Cannons
After the boss you can drag the group in front of the doors that opened to the cannons.
The colossus in front of the gate can be ignored if you sneak along the left side. You don't have to attack it at all. Every DPS should be staying at the cannons here, the tanks will go inside, and grab the monsters that are on the two platforms. They can be dragged back to the cannons for easy killing.
Then the tank goes to turn off the searchlights on the platforms, and use one of the cannons on the airship ONCE. Two collosus will appear. Drag them to the cannon again for easy finishing. Then the path to Livia is clear after destroying the airship with a few more blasts.
Livia Part 1
Let the hands fill the 4 cannons, then do a small countdown and shoot all of them at the same time. Use the 4 DPS for the cannons.
One of the DPS will get hate on Livia, that DPS tanks Livia in the center, while the two tanks and the DPS handle the adds that try to destroy the cannons or the loading hands. After that, load the cannons again and shoot all 4 at the same time again, and the battle is over.
Livia Part 2
Livia will call for reinforcements during the fight, locking on one target at random. They can be slept or kept together for AOE damage, but either way you cannot take hate off the target, you can only handle the DPS as fast as possible. Once the vanguard or reaper appear, off tank it as usual while you finish the boss.