Need help from the pros here for Challenge 6

Let's take a look. First of, I'll give you advice for all rounds. Mostly because making previous rounds go by faster and easier makes you get to the latter rounds better equipped and less mentally drained.

Round 1: Exchange your Assault Rifle for LFE gun. Dash to the spawns and LFE them as the Gorgies spawn. Not too hard. Takes a few tries to get down but takes off a lot of time and chance you'll have to do cleanup afterwards. Viper is indeed very easy. HMG>Shotgun FireCancel deals insane damage. The second he falls to his knees do melee, you'll have recovered before he does from it.

Round 2: Perfect strategy; my personal favorite. Don't take cover behind the statue though, simply stand behind it and take pop shots.
Also nice trick is that you can actually (almost) instakill that Bogey. Once he falls to his knees it's actually possible to headshot him with a boost-melee, the actual tip of the animation has to hit him; so do the attack from a long distance. Even still, a boost-melee deals 40% damage to him.

Round 3: There are a ton of tactics here. Sometimes I just pop a cigar in my mouth and shotgun them all to robot-hell. But that's not the smartest and safest option. You've already found that one; Disc-launcher. Use AR mode to aim for their heads and then take cover somewhere smart.
Basically you start like this: start near the round1 begin point. The second "Challenge6: Round3" dissapears throw a REGULAR grenade into the Gorgie spawn. They'll die. Wait for a few seconds behind cover and let the Flame Romanov get close.
AR-HMG his backpack to kill him. After this just AR-disc some heads and wait for them to suicide (without heads they'll die after a minute or so).

Round 4: start near the beginning again. LFE the rollers as they are vulnerable when they spawn. Quickly go to the outer ring of the level (right to the statue from the starting point) and you'll see a turret spawn. Kill it's pilot. Then quickly focus on the other pilot.
Once those are done it's just you, your HMG-Shotgun combo and two BIA's and a lot of blues.
LFE does wonders against them too, kills blues in about two shots and can seriously stun BIA's. Once all the blues are gone you can use the LFE to stun both BIA's, melee them, LFE them 3 times, melee them again, etc. For the rest keep your distance against BIA's unless you REALLY know what you're doing. They are killer in melee.
This part is a bit of a grind unless you want to use 6 rockets, as these guys have a ton of health.

Round 5: pop an EMP near the start of the level to expose the rollers. LFE them to death. Do NOT focus on the Bogey's until the rollers are gone. After which, it's up to you. The Bogey's are a mission on their own and are set to Hard Difficulty. There's not as much cover as in 5-3 so it's harder.
Play a bit of 5-3 without using cover on hard. Learn their callsigns for attacks and when to use Rockets safely. I can give you tips here, but this part is best left discovered on your own as you really need your musclememory to see you through here.

Good luck!
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PSN: Royta15
www.youtube.com/royta15

What helped me out a lot was realizing just how crap the Lock-on-Launcher was against them. The damage was just too low.
My personal recommendation for the fight is:

* Focus on the Red Bogey. He's the one with the two insane damaging moves (super laser and sniper). Keep your eyes at him at all times and at the Blue one atleast through your radar.
* Keep the Rocket Launcher as a super punish for when the Red Bogey charges his super laser. It should hit him before the laser even hits you and he can't dodge due to him being in that animation.
* Use the HMG and Shotgun combo to kill them. Shotgun does insane damage to them up close.
* You CAN EMP-slide-stun them to death. Use the EMP-slide (Boost+EMP) to get them to their knees, follow up with a HMG>Shotgun firecancel, dodge back, ARS shotgun shot, EMPslide again.

Good luck!
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PSN: Royta15
www.youtube.com/royta15

The LoL has a terrible damage output, and in the double Bogey case you want them dead fast. The HMG does a ton of damage to them, as does the shotgun. Both of which you can easily aim in ARS mode.
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PSN: Royta15
www.youtube.com/royta15

The Vanquish-High, such a unique moment in gaming. Congratulations man!
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PSN: Royta15
www.youtube.com/royta15