Use the following trick to get 6,600 CP in about two minutes. There are two Behemoth-like enemies fighting each other at Gran Pulse. When you encounter them, a preemptive attack will always happen. Use the following Optima set-up - Attacker/Enhancer/Enhancer. Wait until you get Haste and Fire elemental offense. Then, switch to Attacker/Blaster/Blaster. Kill the purple creature to make the white one is easier to defeat. Return near the save point to have them respawn.
Toward the end of Chapter 7, when you are at Hope's home, you will encounter an attack from groups of three PSICOM enemies. There is a save point, as well as a bunch of enemies to the left and right side of you. After defeating one set of enemies, fight the next set. Once you have defeated them, run around the room to the other side and the enemies will respawn. You can continue doing this and complete a battle each time under one minute by simply using the Relentless Assault and Diversity combinations. After each battle, you will receive 160 CP, as well as occasionally an item from the spoil that remains. By doing this, you can easily gain enough CP to use later on if you have already maxed out your current level, or you can max out your current level in the Crystarium system.
When you first arrive in Gran Pulse (Disc 3), you will be told to go to Vanille's village. On the way to the village, you must go through a tower called Taejin Tower. Do the following steps there:
1. Defeat the Boss at the apex of Taejin Tower. 2. Take the elevator down to level four, and then the other elevator (the first room on the left when exiting the elevator) up to level 5. 3. You will see a mission statue directly in front of the elevator (mission 24) 4. Select the statue and re-accept the mission. The target will spawn in the same room. 5. Kill the group of three that spawns and get 6,000 CP and an item that sells for 6,000 Gil. 6. Go back to the statue, re-accept the mission again and complete it. Repeat the steps as desired.
You can use the following strategy and kill them in about 34 seconds with tier two weapons. Have your party consist of Snow, Vanille (use her tier two Marlboros Wand), and Lightning. Tactics: Default - Ravager, Ravager, Ravager ---- Other - Commando, Saboteur, Commando. Open up with the default Ravager x3 on the main target (in the middle and should be auto targeted) until he is staggering. Then, switch to your other tactic and continue auto-attacking the same enemy. With the help from Vanille (saboteur) he will die in a few combos while your other commando is already killing one of the side enemies. Keep attacking until he is dead. To make this easier, have the auto-haste gear called "Sprint Shoes" equipped.
During the assault on the Estheim house, run around the circular hallway instead of taking the red circle out of the room. The soldiers aren't hard to defeat, and you can gain anywhere from 120 to 200 CP per battle, as well as an incentive chip, which you can sell if desired. The simplest way to do this is to attack the soldiers at the window. Rather than turn around and go straight for the soldiers behind you, go around the hall and attack. By the time you make it back, the soldiers at the window will have respawned.