After you killed Anima, it granted you a mark and whoever has the mark is called l'Cie, basically you are a slave of the fal'Cie. However, with this mark comes with great benefits as well as you now have access to magic and other abilities via Crystarium.

A lot of things will happen during this battle and the introduction to Paradigms. In a simple term, paradigm is a set of roles that you predefine in the menu for each character and each character comes with two default roles. For example, Lightning has "Commando" and "Ravager". During the battle, you can switch between paradigms for better offensive or defensive strategy. 

Take left turn at the fork.

• ENEMY (E-01): Ghast (x3)
• ENEMY (E-02): Ghoul (x4) (LAST ENCOUNTER), Ghast (x1)
• WEAPON (T-01): Pearlwing Staff (x1)
  Go ahead and equip it on Vanille, also Iron Bangle too.

Backtrack and go on the other path.

• ENEMY (E-03): Wight (x3), Ghast (x1)
• ITEM (T-02): Chipped Fang (x7)
• ITEM (T-03): 200 gil
  (Side area to your right)
   
• ENEMY (E-04): PSICOM Warden (x4)
• ENEMY (E-05): Wight (x3) (LAST ENCOUNTER), Ghast (x3) (LAST ENCOUNTER)
• ITEM (T-04): Cie'th Tears (x5)
• ENEMY (E-06): Breshan Bass (x4) (FIRST ENCOUNTER)

When you reach a fork, go left:

• ENEMY (E-07): Breshan Bass (x4)
• ACCESSORY (T-05): Silver Bangle (x1)

Backtrack to the main path:

• ENEMY (E-08): Pantheron (x4)
• ITEM (T-06): Phoenix Down (x1)
• ITEM (T-07): 50 gil
• ENEMY (E-09): Pantheron (x2)
• ITEM (T-08): Strange Fluid (x8)
• ENEMY (E-10): PSICOM Enforcer (x2) (LAST ENCOUNTER), PSICOM Warden (x1) (LAST ENCOUNTER)
• ACCESSORY (T-09): Magician's Mark (x1)

When you reach another Save Point, prepare for another tutorial boss fight. It basically teach you how to switch between paradigms. This fight is a little bit harder than the first encounter because it forces you to shift to a different paradigm to heal when your party is low, then shift it back for offensive.

Go to menu -> Paradigms, then setup the following (Lightning/Vanille/Sazh):

• COM/RAV/RAV
• COM/MED/RAV

• BOSS (B-01): Manasvin Warmech (x1)
  Strategy: Just switch back and forth between the paradigms.

Equip Silver Bangle on Sazh and continue.

• ENEMY (E-11): Breshan Bass (x3)
• ITEM (T-10): Strange Fluid (x6)
  (Right path)
   
• ENEMY (E-12): Pantheron (x4)

There are 2 paths, take the left one.

• ITEM (T-11): 240 gil
• WEAPON (T-12): Deneb Duellers (x1)
  (Equip it on Sazh)

Backtrack and go to the right path.

• ENEMY (E-13): Bloodfang Bass (x5) (FIRST ENCOUNTER), Breshan Bass (x1)

Take the right path.

• ENEMY (E-14): Bloodfang Bass (x4), Breshan Bass (x1)
• ITEM (T-13): Enigmatic Fluid (x6)

Backtrack and continue the main path you will see a yellow dot on the map, examine it to open the a new path in front.

At the dead end is 4 Pantherons and an item:

• ENEMY (E-15): Pantheron (x4)
• ITEM (T-14): Wicked Fangs (x7)

Continue on the main path.

• ENEMY (E-16): Bloodfang Bass (x7) (LAST ENCOUNTER), Breshan Bass (x3) (LAST ENCOUNTER)
• ENEMY (E-17): Alpha Behemoth (x1) (FIRST ENCOUNTER)
• ITEM (T-15): Librascope (x1)
  (Side area to your right)
   
• ENEMY (E-18): PSICOM Tracker (x2) (FIRST ENCOUNTER)
  ENEMY (E-19): Watchdrone (x3) (FIRST ENCOUNTER)
  ITEM (T-16): Digital Circuits (x2)
  (side area)
   
• ENEMY (E-20): PSICOM Tracker (x2), PSICOM Ranger (x1) (FIRST ENCOUNTER)

Take the right path.

• ITEM (T-17): Paraffin Oil (x2)
• ITEM (T-18): 50 gil
• ITEM (T-19): Insulated Cabling (x3)
  (Side area to your right)
   
• ENEMY (E-21): Watchdrone (x1), Ciconia Velocycle (x1) (FIRST/LAST ENCOUNTER)

• ENEMY (E-22): Watchdrone (x3)
• ITEM (T-20): 30 gil
• ITEM (T-21): Begrimed Claws (x6)
• ITEM (T-22): 600 gil (side area)
• ENEMY (E-23): Alpha Behemoth (x1)
• ENEMY (E-24): Watchdrone (x3), PSICOM Ranger (x1)
• ITEM (T-23): Digital Circuits (x2)
• ITEM (T-24): Begrimed Claws (x7)
• ENEMY (E-25): Crusader (x1) (FIRST ENCOUNTER), PSICOM Ranger (x2)
• ENEMY (E-26): Crusader (x1) (LAST ENCOUNTER), PSICOM Ranger (x2)
• ITEM (T-25): Spark Ring (x1)
• ITEM (T-26): Potions (x3)
   

• ENEMY (E-27): Pantheron (x2)
• ENEMY (E-28): PSICOM Ranger (x2), PSICOM Executioner (x1) (FIRST ENCOUNTER)
• ENEMY (E-29): PSICOM Tracker (x2), PSICOM Ranger (x1)
• ITEM (T-27): Millerite (x1)
• ENEMY (E-30): Pantheron (x2), PSICOM Tracker (x2), PSICOM Ranger (x2)
• ENEMY (E-31): Pantheron (x3)

Take the stairs on the side.

• ENEMY (E-32): PSICOM Tracker (x1), PSICOM Ranger (x1)
• ITEM (T-28): Ferroelectric Film (x1)

Then you can just jump down.

• ENEMY (E-33): PSICOM Tracker (x2), PSICOM Executioner (x1) (LAST ENCOUNTER), PSICOM Ranger (x1)
• ITEM (T-29): Phoenix Down (x1)
• ITEM (T-30): Librascope (x2)
     

Now it is time to use your Crystarium Points. Open your menu -> Crystarium:

• Lightning: Max out Commando then Ravager.
• Vanille: Max out Medic then Ravager.
• Sazh: Max out Ravager.

Be prepare for a boss fight. Go to menu -> Paradigms, then setup the following (Lightning/Vanille/Sazh):

• COM/RAV/RAV
• COM/MED/RAV

• BOSS (B-02): Garuda Interceptor (x1)
  Strategy:
  • Start with COM/RAV/RAV and throw 1 Libra.
  • When you health bars are low, switch to COM/MED/RAV to heal then switch back COM/RAV/RAV for offensive.

Back to our tough guy alone at the Lake Brasha. You start with an unwinnable battle. After the battle, watch a cutscene for an introduction to a new battle mechanic, Eidolon, and a glimpse of a new character. For this and any future battles with eidolons, your goal is not to kill them (You cannot kill them anyway) but to impress them enough to fill out a purple gauge within a countdown time. Well, if you can't fill out the gauge in time, you die, simple as that. Now in order to quickly fill the Gestalt gauge, you cannot use "Attack" command alone, you are requires to use different abilities. It doesn't matter if it is offensive or defensive skills, the trick is how you mix them and use the skills in different situations.

• EIDOLON (B-03): Nix (x1)
  Strategy: 
  • Start by casting 1 Libra on Nix.
  • Whenever you see "ATB Charge" on her head, immediately switch to SEN and press Auto-battle. After she attacked you, you'll see the gauge fill up pretty quick.
  • Switch back to COM or RAV when she is not using "ATB Charge".