There are no collectibles in this mission so you don't have to bother exploring every nook and cranny of the area. Follow Kat and wait for her to spray a circle on the steel pillar. Use demon pull on it and the other pillar she marks. Once the entrance is blocked, follow her then use demon pull on the wall to reveal an old tunnel behind it.
Keep following her until she hides but gets spotted by a SWAT member. She'll mark an equipment so stay close to that and wait until the enemy is beside the equipment before pulling it.
Continue following Kat until you find Vergil in the large hall. Destroy the bladed butcher to rescue him then buy them some time by fighting off waves of demons. After defeating rage spawns and demon shards, Vergil will give you the Revenant – perfect for one-shoting those pesky demon shards.