When you are at Hope's home towards the end of Chapter 7, you will
encounter an attack from groups of three PSICOM enemies. There is a save
point, and a group of enemies to the left and right side of you. Defeat
one set of enemies, and then fight the next set. Once you have defeated
all of them, run around the room to the other side, and the enemies will
respawn. You can repeat this as many times as desired and complete a
battle each time in under one minute by simply using the Relentless
Assault and Diversity combinations. After each battle, you will get 160
CP, as well as an item occasionally from the spoil that remains. This
trick allows you to 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 Crystalium 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 Taejin
Tower. Do the following steps there to get easy CP:

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 five.
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 spawn to 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 these steps as many times as desired. 

You can use the following tactic to kill them in approximately 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. Start
with the default Ravager x3 on the main target (in the middle; should be
auto targeted) until he is staggering. Then, switch to your other
tactic, and keep auto-attacking the same enemy. With 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 "Sprint Shoes" gear 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 are easy
to defeat, and you can get anywhere from 120 to 200 CP per battle, as
well as an incentive chip that you can sell if desired. An easy way to
do this is to attack the soldiers at the window, and instead of turning
around and going straight for the soldiers behind you, go around the
hall and attack. Once you make it back, the soldiers at the window will
have respawned.

When you enter the hall while on the Palamecia and the alarms go off
(there is a safe point against the wall), defeat all the enemies.
Instead of following the right turn, keep going. You will eventually end
up back at the entrance to the ship. Kill all the enemies located there,
then turn back. The enemies in the hall will have respawned. Most
battles will get you at least two Credit Chips or one Incentive Chip,
and a good amount of CP. Repeat this as many times as desired.

Use the following trick to get 6,600 CP in approximately two minutes.
There are two Behemoth-like enemies fighting each other at Gran Pulse.
Once 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
easier to defeat. Go back near the save point to have them respawn.