In this chapter, there is total war, total destruction, and it's totally awesome.
Move forward and across to talk to a soldier.
Head across the bridge, picking up ammo along the way. Kill every Daemon that stands in your way. From here on out it's one crunchtastic blood fest. Take out the Tainted Psyker so your accompanying forces can move forward.
It's the same deal with this fight, except without the Tainted Psyker and with a considerable larger force. When they're dealt with, run forward and use the Autocannon to kill the three Tainted Psykers that just spawned, as well as the Chaos Drones who come over to annoy you. Run forward to the Valkyrie to trigger a checkpoint and a cutscene.
With the Jump Pack and Thunder Hammer in hand, keep up your slaughter count. Run through the ruined Spire and destroy everything. Notice how effective the Thunder Hammer is against Bloodletter Daemons!
Jump from platform to platform and take out any Daemons standing in your way. You'll eventually hit a checkpoint.
A Chaos Space Marine should be shooting at you from a high platform. Jump up to him and teach him a lesson. Pick up another Servo Skull (Inquisitor Drogan 10/10) on that same platform, then advanced toward a broken staircase. Jump over it and kill everyone. Your Jump Pack should have conveniently run out of fuel again.
Continue forward and pick up some ammo. Open the door in front of you and kill the Chaos Drone that just spawned. Head right to pick up a Servo Skull (Under Attack 3/3) then head left again. Keep running.
You should have a new objective: Hunt Down Nemeroth. Keep running and kill the Chaos Space Marines shooting at you upstairs, as well as the Bloodletter Daemons on the ground floor and the Renegades to your right.
Keep killing. Proceed forward until a Tainted Psyker spawns, then kill him too. Go up the stairs, to your right, then forward again. Activate the lift.
We're almost there! Just keep running...
...and running. Grab whatever weapons you want and get ready to hunt down Nemeroth. Run forward to complete the chapter.