Here's a strategy:
1-1
Just bring a Rocket Launcher, a Shotgun and an attache case full of herbs. Equip the Rocket Launcher whenever you run, constantly tap Select, dodge past the first Majini and when we get to the Public Assembly, run to the safe corner on the left and cover both spawn points with the RLs, if they get too close use the Shotgun. When the Executioner destroy the gate, vaporize him and then run into the new area to stop the infinite time glitch. We either run back to where we were or head for the roof. Wait for Mi- Kirk.
1-2
At the very start, follow me so that we avoid the cutscene showing the ladder. Run past everything from then on, tap select when we break down the door, when we are in the building to avoid the 'scream' cutscene, when we break down the second door. One of us should wait in the room Uroborus appears in, while the other grabs the Furnace Key. That may save some time. Use the RL to finish the battle straight away. Run to the elevator and tap select to finish the cutscene.