Final Fantasy XIII/Post-game

After you have beaten the game storyline, watched the credits and saved, when you next restart your game you'll find yourself in the hallways of Orphan's Cradle, right before you fight the final boss. You can fight the end fight as many times as you want, and you can also use the warp to back to the beginning of Orphan's Cradle where you'll find warps to both Eden and Gran Pulse. In-game reasons for continuing to play would be to finish the Missions, complete your Crystarium, unlock other areas of the game or max out your Weapons. Outside of the game, you may also be attempting to earn achievements or trophies, some of which can only be obtained after beating the story portion of the game.

Your priorities for post-game play are to obtain the Growth Egg and get your party to the point where they can most efficiently farm Adamantoise. There are a few spots where you can effortlessly grind for CP, but none of them can compare with the drops you'll receive from Adamantoise, namely Platinum Ingots worth 150,000 Gil apiece and Trapezohedron's, the catalyst needed to upgrade all weapons to their ultimate forms. The Growth Egg, obtained from completing Mission 55, will double the CP awarded to your party, which results in 80,000 CP for each Adamantoise.

Outlined here will be explanations on the remaining optional areas and sidequests you embark upon, and strategies for getting your party to the point where they can handle what comes, as you'll be facing the hardest battles at this point.

Farming
Farming is the act of constantly fighting an enemy or route full of enemies over and over hoping to gain certain elements, such as CP, high Gil components and catalysts. You will have already obtained all the weapons and most accessories by playing through the story, and you can acquire certain rare accessories through Missions, so these are the three things you'll want to farm in order to level up your characters and equipment. Although there are places where you can find some good farming during the story, you are in inhibited by the capped Crystarium and you don't need to upgrade anything until post-game anyway.

Equipment you will want to maximize your spoils are:
 * Growth Egg: Doubles CP
 * Connoisseur Catalog: Increases rate of rare drops
 * Collector Catalog: Increases rate of normal drops
 * Survivalist Catalog: Increases rate of shroud drops

When you defeat enemies, the game checks your rare drop roll first, followed by the normal drop roll if you don't get a rare drop. Shroud drops are checked independently. In most cases you will want the rare drop more than the normal drop, so you can equip all three catalogs. In the rare instances when you don't want the rare drop, unequip the Connoisseur Catalog.

Mah'habara is the location of the mines where you rode Atomos on your way to Oerba in Chapter 11. In Mah'habara there are a few places where you can fight multiple Cryohedrons, which at this point can be killed very quickly. The best spot is where you can bounce back and forth between a group of Cryohedrons and Rust Puddings, both of which will have respawned by the time you get back to them. The Rust Puddings (group of two) will drop around 6,000 CP and the Cryohedrons (group of five) will drop around 12,000 CP, assuming you have the Growth Egg. This is a really boring, but is a very easy, low risk way to earn CP and Bomb Cores (Cryohedron rare drop) have a pretty good sell price at 600 Gil.
 * Mah'habara

Just outside the entrance to the mines, you'll find a Behemoth King roving around above a path leading down to another Behemoth King locked in combat with a Megistotherian. When you first come to Gran Pulse, the lone Behemoth King is a great way to grind for CP, as its 4,000 CP prize is unmatched for the rest of the game when you consider how quickly they can be taken down with a pre-emptive strike. Start out by farming this lone Behemoth King by getting a pre-emptive and laying into it with a couple Commandos. A paradigm like will allow your Ravager to complete the stagger while your Commandos launch the beast and kill it.
 * Northern Highlands

Once you have a character with over 2,000 strength (usually Fang), and two others with over 1,200 (usually Lightning and Snow), you can start taking out the two large creatures down the path. You'll want to put your strong character on the far right of your battle team with the Morale Talisman equipped for Auto-Bravery. Due to the AI mechanics, your party leader and the middle battle team member will fight the Behemoth King, while the far left character takes out the Megistotherian. When you enter the battle (automatic pre-emptive, since they're battling each other), you'll put their stagger percentage up so high and they start with half health, that it will only take one round to take them out. You only need the paradigm, and the battle should only take six seconds. Afterward, run back up the hill past the save point to the Chocobo and then back down to reset them. This will net you around 13,000 CP for very little work.

This area is only accessible by Chocobo and can be reached by jumping up the cliff behind all the Navidons by the ring of seven C'ieth stones on the eastern side of the map. When you get to the open area with the save point, you can start fighting the Ochu and his Mirochu minions. With the Growth Egg, this group will drop over 25,000 CP and some great components for both trading for Gil and for boosting the experience multiplier when upgrading. The downside to this area is it will take a more complicated strategy. Unlike the Japanese version of the game, you can't get a pre-emptive strike on these enemies, so you'll have to have the right equipment and paradigm deck.
 * Paddra's Pasture

The basic strategy is to buff your high strength character (usually Fang) and let her take out the Ochu and then finish off the little guys. Once you have a lot more HP (over 15,000 on each character), you won't have to worry about healing anymore and can just go in and finish them off quickly. You'll want to use the Moral Talisman on Fang for Auto-Bravery, and Aurora Scarfs on everyone for Auto-Haste so your Synergist doesn't have to spend time on it. Tetradic Tiaras for everyone and strength plus accessories for Fang will also help. To start, have Fang attacking while two Synergists quickly buff your party (Sazh and Hope, since they are Synergist primaries). Once Fang has Enfire and Vigilance, switch to a more offensive paradigm, optionally leaving one character as a Medic if you don't have high HP. Make good use of ATB switching between identical paradigms to speed up the ATB refill.

Here is what your paradigm deck might look like:
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As an alternative method, you can try starting with to debuff the enemy (with perhaps Fang, Sazh, Vanille) instead of using two Synergists.