Final Fantasy XIII/Chapter 2: The Pulse Vestige

Sacrarium
After a cutscene, you'll battle a Pantheron with Vanille and party member Hope. Before going up the stairs, go backwards for an item container containing 30 gil. You will then be told about preemptive strikes. Certain enemies, like the Zwerg Scandroid, have narrow fields of vision, allowing for an easy preemptive strike. A group of three Zerg Scandroids guarding an Iron Bangle will be in front of you for practice. Two Pantherons will also be ahead. Following those will be a cutscene, which will bring you to Snow's point of view.

House of Stairs
The path here is very straight-forward. After defeating two Pantherons, activate a switch. After a cutscene, you'll be brought back to Lightning and Sazh, who have also gotten into the Pulse Vestige.

Ambulatory
Before you play, you'll be told about shrouds. To the right is a Save Point and three Pantherons will be running down the stairs. After defeating them, walk up the stairs to see three groups of enemies: four Zwerg Scandroids on the left, two Pantherons in the middle, and three Zwerg Scandroids on the right. After following the main path and encountering two more groups of enemies (a Myrmidon and Pantheron/Myrmidon group) there will be a cutscene.