This will pop after you defeat the Lambent Leviathan as Marcus's group of COGs in Act 1.
I did this on Hardcore difficulty in Standard mode.
The main trick to clearing this area is using the Silverback's rockets. After helping the Ravens liftoff and navigating through the flaming gardens, you'll come across a garage with 2 Silverbacks.
Climb into one using X (don't forget the instruction manual collectible) and make for the gate a bit further down. Press B as prompted to knock the gate down and reveal your leviathan foe.
As with the last time you met such a beast, the leviathan will be trying to chow down on your vessel and you need to drive it off before it does.
Hunker down by tapping A (holding A will just have you running) and press RT for rockets. Aim for the eyes mainly and the mouth as you may be prompted. Aiming reticle turning red is usually a good indicator. ;>
This will be timed so don't dilly dally with the other lambent too much when the leviathan is present or you'll see a giant maw coming down on you. ;)
After a few hits (seems like 5-10), the Leviathan will rear up and break off for a while during which a wave of lambent grunts will keep you occupied.
Repeat process when leviathan returns and you'll stay alive.
I'm guessing you do this 3 to 5 times. I didn't count as well due to listening to the communications going on.
The whole sequence is kind of scripted as Marcus will be communicating with Cole's team up on the bridge above as you fight. After the series of communiques, the battle will end with Cole's team sending a bunch of tickers down on the leviathan's head.
The game will take care of saving Marcus's group by sending them overboard into the water and you will have to wait until after we see Cole's story before we find out what happened to them.