I've had it!

At first I didn't think I'd have to put out a guide on how to consistently do twins FAST. But not only are there NO guides out there, there are no other players (as of today) that think they can control the speed at which this boss can be killed. So here's the link to the "New Recruits" thread I made with the video link inside.
I choose the "New Recruits" thread because new players will want to understand how to beat this boss quickly just as much as the experienced players. I also have a bonus clip of how to stop Snarbolax from trolling you =)

yup, Romulus twins need no weapons, just good armour and dodging skills... Shield users UNITE!!!!

If you have good dodging skills you don't need the armor either.
Twins can beaten with nothing but a proto sword. Have fun getting there, though.

You certainly could, but you do need to attack the twins then they're down. Might be more tedious than anything. And the scuttlebots do like to irritate you.

I know RT well... well enough to be able to do no-hit solo runs. I like it more than JK, but due to the lower crown output I stopped doing it after I get pulsar and catalyzer.
I always take Polaris to RT, so I never noticed that you can shoot that switch on the first missile wave. Since I only need one sword (DA) and one gun there, I'll take Silversix there as well next time.

Very nice! I'm impressed with your timing

No-hit runs: Practice makes perfect. :D Even when you are stuck with a red dot connection (I am).
- Solo. For lowered monster health, and avoiding people accidentally hitting switches or blocking a rocket near you, blasting you with the area damage.
- Be very familiar with mecha/gremlin/quicksilver attack patterns so you can predict and avoid them.
- Pulsar line to make puppies shut up.
- Elemental sword to kill mecha. I prefer Divine Avenger over Brandish line, because I use the knock back to interrupt and keep me safe.
- Shadow weapon for the few gremlins and quicksilvers. Again I prefer Gran Faust over Brandish line, for the knock back and interrupt.
- I can also use Divine Avenger instead of shadow weapon by making use of the knock back.
- A good shield. Grey Owlite is the best here.
- Quicksilvers are the main threat here (not a threat that can kill you, a threat that may break your shield and hit you). Kill them first.
- Note that mecha knights can hit switch with their attacks. You'd want to flip it back quickly.
Now to some tips for each particular sections...
Missile alley at the start:
- Use gun to clear the bombs away first, so you have a place to hide as you move up. Polaris has the range advantage among the guns.
The 1st level room with the group button in the middle, left and right section divided by walls and enemies spawn in waves:
- You can minimize the amount of enemies to fight by using the walls to lock them out.
- Do the sections in an alternate pattern. Right after you trigger the button, move to the right section and seal it. Clear enemies there. Then left. Then right. This pattern locks the quicksilvers away from you when they spawn.
The shock + missile corridor leading to the last room:
- You can turn off the shock from outside.
- First, trigger both red buttons on both sides.
- Go back to the top end of the right side, grab a pot along the way.
- Throw pot at the two switches.
- To aim, put your cursor directly on top of the switch.
- Pulsar line can hit the switch closer to you.
The last 1st level room, with rockets shooting from the top and both sides:
- Keep the walls purple, that is to block missiles from left and right. The top missions shoot on the left and right parts of the room, so when the alarm sounds, stay in the middle.
The room with three red buttons and quicksilver spawning:
- Seal the door to block rockets from the left.
- Trigger buttons from left to right.
- Immediately after pressing the last button, run/shield-move to the dead-end corridor on the right.
- The narrow opening means berserk quicksilvers have very little chance to get inside. They will have to move to you slowly.
- Take them out inside, one by one.
The room filled with bombs:
- You can clear the bombs yourself, but I see most people get distracted by all the effects and end up getting hit in the back by a missile. Or get into the blast radius of a bomb.
- Instead, let the missiles clear the path for you.
- Stay near the top at the start. Dodge the missiles by moving left and right.
- Slowly move down, be sure not to get too close. You don't want to get inside the bombs' blast radii.
The next corridor with regenerating blocks and missiles:
- Shoot blocks while the missiles are blocking your path in front of you. Move across right after.
The next room, with rows of missiles on the left, gun puppies/retrodes/mecha knight/scuttlebot as enemies:
- Stay on the right side. If your latency is not low, it's best not to tempt fate and mess with the missiles.
- The first gun puppy appears after you kill the scuttlebots, one a spot north of the group button. Prepare to wipe it out immediately.
- Along with the first puppy there will be two retrodes. Dodge their ray, move into mid-range. They will try to move closer to melee you. Back away to the right. Draw them out and kill them in the missile-free area.
- The next gun puppy appears to the right side of the group button. Prepare to wipe it out immediately.
- Dodge the retrodes and kill the mecha knight first. Then draw the retrodes out.
Choose a path:
- Choose the lower path, but don't step on the group button yet.
- Go back and grab a pot.
- Once the missiles start firing, hit the switch to the far top with the pot. Aim by putting cursor right on top of it.
- Now you have the lower path missile-free.
Last room before boss fight:
- Before stepping on group button, use heavy swords or bombs to break as much blocks as you can.
- Ignore the mechas.
- Time it right - before the moment you need to move in and hit the switch, stand still and bait the mechas to attack. When they prepare to attack, you move away, ready to hit the switch.
- The left button shuts off the retrode and mecha knight. The right button shuts off the scuttlebot.
- You may want to shut off the left one first. Then kill the retrode and mecha knight first. This keeps you from fighting all three mechas and two gremlins together.
Boss fight:
- Watch out for the shock orbs. Missiles and bombs are flashy and obvious, it's the subtle orbs that may get you.
- Clear only the blocks in the central column. Let the corner blocks trap the scuttlebots for as long as possible.
- Don't let all four scuttlebots out to play - four is too many for a single knight. They take a while to regenerate, so when there are more than two chasing you, take a break from the twins and wipe them out first.
- Watch out for scuttlebots, even when you are attacking a vulnerable twin. Better to stop early than to risk getting shocked.

The 1:23 attempt done in the video was also a flawless (no damage taken) run.
I have a run done in full 2* gear that goes virtually hitless too done as a really old guide. I made those videos not long after I started playing and its about 5 months old too.
Very nice. I thought I knew RT very well, but this will help me in future RT runs. (:
Something else that helps out too: I found that the twins become vulnerable as soon as a missile hits them. However, they won't fall down until they stop attacking. If you hit a twin while it's vulnerable and it's attacking then you'll interrupt its attack and cause it to fall. Normally this doesn't speed things up much. But, you can use this technique to interrupt the laser attack and speed things up more.
I also like what you did with the graviton bomb/vortex on snarby. I did not know that could be done until now. (=