For multiplayer, you can also use pipes and a HUcast (maxATP/ATA) with Dark Flow (sphered) to make this faster. (as long as the HUcast has 20Shifta, 12.5% HP or less at all times and an invincibility mag)
To explain:
In forest, it is faster if the HUcast receives Shifta at the start and ignores the Hildelt, allowing the support (preferably RAmarl) / other people (if more than 2P) to kill it. In the next room, ignore the minimum kill Booma, and allow the HUcast to NHH all enemies. Use a Freeze Trap on the Hildelts and detonate it when they can be attacked, then NHH them to kill. This should get you into the warp a couple of seconds faster than waiting for the Booma and running all the way.
At the dragon, someone should drop him as soon as possible using any method you see fit. When he is down, everyone except the HUcast should run to the warp location for Caves. The HUcast himself should berserk himself down to as little HP as possible (3). When the dragon is rising and is targettabled, the HUcast uses Flow's special when stood RIGHT next to the feet. This will OHKO the dragon and it will not even fly off.
Caves is simple, follow it normally, but in the room in which you wait for the vulmer, everyone except one person should run to the boss door. The person staying should lay up a pipe and wait on it while waiting for the Vulmer. When the Vulmer spawns, kill it and pipe up immediately. The people waiting at the boss door should lay a pipe, with the person who killed the Vulmer piping down.
De Rol is simple; the HUcast starts with flow special (hopefully invincibility kicks in!), and when DRL lands, Excalibur is used (preferably with AB/H). Another person should help kill DRL (so 2 at least), while the others wait at the warp to mines.
In Mines, RA should freeze sinow with Shooter, others should run ahead. One person kills the canadine, one person calls the sinow, one person kills the sinow. Then everyone runs PAST the Baranz together. A CAST should lay a Freeze Trap. IGNORE the Dubchich. Instead, get a RA to CR the dubswitch. Try to stand at a range from it, you don't need to go up close to it.
At Vol Opt, the HUcast should be running around to keep his HP down (auto-HP recovery), while a FO/RAmarl/HUnewearl stunlocks Vol Opt with Excalibur, V801 and Gizonde (make sure the pillars DO NOT come up, or the HUcast will die if invincibility has not kicked in). For phase 2, attack the part in front of you. The HUcast should stand right next to Vol and SSS with Flow. He should die quickly.
In Ruins, allow the HUcast to Flow the Bringer. This will OHKO it. One person (preferably RA with Dark HS) should run past the Arlans for the extra spawn, killing the sorcerer with HS on the way (a CAST should FT the Arlans they run past, so they are not interrupted). The rest of the people should run for the boss, killing the Arlan on the way. Here, the person who called the Arlan should pipe up, and wait for one of the people who ran to the boss to pipe up themselves.
For Falz, kill darvants as normal. The HUcast should try to situate himself where Falz' first head drops. When Falz spawns, support should Zalure and then everyone SHOULD NOT attack, except the HUcast who will SSS on the Falz' head which is on the floor (you can try to kill the darvants if you want if you're not the HUcast). Falz 2 should be plugged using mechguns (preferably charge), Falz 3 the same. Try to be split during Falz 3, don't camp at the RR drop spot, so you can maximise damage no matter where Falz is.
And, that's about it. You can replace HUcast with any HU if you want, I just used HUcast as an example.
Here's a video showing a TTF like that: (Not me, some people I know)