From the initial entrance, go up and turn right down through the first camp to the cave entrance. Head into the cave tunnel system. Fight your way through keeping to the upper (right) side of the cave system. After getting through there, keep heading up: you’ll pass through a small open cave, then head up the metal staircase. You’ll come into open air in a small ravine (couple of super badass psycho spawns); just keep following the linear path forward and ignore side paths till you get to the main camp in a deep wide valley. The place you need to get to is straight across from the descent into the valley, but you’ll need to clear a ton of bad guys out of the way. What you’re looking for is a cave entrance on the far side with icicles hanging down in front of it. Pass through the cave system avoiding the traps (keep an eye out for big black scorch marks!), cross the narrow bridges, and you’re at the vending machines outside the lair.
Hint: There are big arrows (the ones with the light bulbs) and overheard hanging markers (the skull-in-the-tire things you can ignite with a fire weapon) as well as the pinned up bodies of Firehawk worshippers all along the route.
Edit: If you’re looking at the full map, then the most obvious route to the lair (straight north-east) is the wrong way. The correct sequence is Blisterpus Camp > Blacktoe Cavern > Ashmouth Camp. It’s a little confusing because the map crosses over itself in the middle (think of it as a giant figure-eight Scalextrik race track!)