Final Fantasy XIII/Chapter 4: The Vile Peaks

Your first battle will be fought with Lightning, Sazh, and Vanille against a group of four Pantherons. The group of l'Cie is then split into two when Lightning walks off and Hope follows her, leaving Sazh and Vanille behind. The new party is Sazh and Vanille.

Dismal Dunescape
Walk a bit down the walkway and you'll come across another one, where a cutscene takes place. You'll see a small flashback to Day 11 and then the point of view will switch to Lightning and Hope. A primer will show you the importance of the Synergist role, a role Hope has access to.

Wrack and Ruin
The first battle you'll come across is one against a Thexteron on the path to the right. Defeat it and open the item container for a Librascope. Go back and then to the left path to fight two Pantherons and a Thexteron. After a lot of jumping will come a battle with three Watchdrones. Keep following the path for the next fight, a Thexteron and two Watchdrones. This battle can be a bit tricky, so make sure you start it off with the Supersoldier paradigm (Commando and Synergist). Then switch to Yin & Yang (Ravager and Medic) and eventually Slash & Burn (Commando and Ravager). Jump up for the next fight with a Pulsework Soldier. This enemy can be a challenge if you don't stagger it, so be sure to make that your goal. Afterward, jump down the cliff for a cutscene and then a flashback to Day 13. You will then go back to playing as Sazh and Vanille. Two primers will show the importance of the Synergist role, a role Sazh has access to, and three-way battles, battles fought between two different factions of enemies and you.

Another Man's Treasure
Go through the tunnel to find your first three-way battle. One Pulsework Soldier will be fighting three Watchdrones. You'll be able to get an easy Preemptive Strike here since the two factions will be focusing on fighting each other. Help the Pulsework Soldier fight the Watchdrones and then turn on the already-weakened soldier when the Watchdrones are defeated. This should make the battle a lot easier, but if you still need a boost, switch to the Tide Turner paradigm (Synergist and Saboteur). After the battle, activate the machine in front of you to open up a new path. The next battle will be another three-way one between two Thexterons and a Pulsework Soldier. Again, get a preemptive strike and work together with the Pulsework Soldier, then turn on it. At the next tunnel will be an item container you have to get open by defeating three Watchdrones, two Thexterons, and a Pulsework Soldier. Defeat the five PSICOM creatures and then the Pulsework Soldier, then open the item container for a Black Belt. Head to the end of the battle for another opened path and a battle between two Pulsework Soldiers and three Thexterons. This time, go for the Pulsework Soldiers and then turn on the Thexterons.