Final Fantasy XIII has a unique and addictive battle system, along with a number of sidequests to enjoy once you reach Pulse. This page will tell you more and includes tips for your next playthrough.
The key to FFXIII's battle system is the paradigm system, which I discussed briefly in the introduction. To start with, there are six different roles; each character has three default roles they're best in, and after chapter 9 they have access to all six roles.
Now, each character can only use one role at a time, and when you want to switch roles, you need to have a paradigm set up, which you can do in the menu outside of battle. The paradigms you have set up are called your paradigm deck. Generally, the deck you have will be based on how far you are in the game and what the characters in your party are; early in the game when you only have two characters at a time, your options are limited. Once you get full choice of party, things are easier.
While there's no perfect set that will defeat every single enemy in the game (which is a good thing!), here are some suggested paradigm decks and party configurations for you. Party leaders and default paradigms are marked.
An excellent, well-rounded deck that can take nearly anything the game throws at you. Relentless Assault serves as the default paradigm unless you're up against very weak foes, in which case Aggression is better so Lightning can use Blitz. Switch to Delta Attack if the enemy is particularly tough, with breaks for Combat Clinic for quick healing as necessary. Evened Odds can give you a boost, and is another good default paradigm. Mystic Tower should be used along with Delta Attack for quick staggering; switch to Mystic Tower when the stagger gauge is about 30% full and you'll find it a breeze to fill it the rest of the way against most enemies.
If you're facing more difficult enemies, swap Aggression out for Solidarity (COM/MED/SEN) to better stay alive.
Lightning/Fang/Hope is the main party I use, so I don't have much experience with other party configurations; however, the official guidebook has a few other suggestions.
A very different set, but no less effective if you know what you're doing. Tri-Disaster will skyrocket the chain gauge into a stagger in no time, provided you can stay alive long enough to do it. The other paradigms take advantage of Hope and Vanille's excellent Synergist and Saboteur skillsets, which buff and debuff the party and enemies, respectively. This is a set that won't get you as quick a victory, but it'll work just as well as the first set.
The key to the paradigm system is to experiment and figure out what works for you. You can make almost any party configuration work if you've got the right paradigm deck to go with it.
FFXIII is often decried as too linear, but the truth is that there are a number of sidequests to do once you reach Gran Pulse. Most of them are done through the Cie'th Stone missions, activated through the stones you find scattered all over Pulse. These stones will lead you to an enemy you'll have to fight, and in some cases, an extra scene or two.
Several of the Cie'th Stone missions are required to complete the game (those in Taejin's Tower), while others are part of another sidequest (Titan's Trials). You can find out more about the Cie'th Stone missions on the achievements page, as completing them will net you achievements or trophies depending on your console.
In FFXIII, your characters start with basic weapons, which can be upgraded to increase their power. While you don't need to upgrade a single weapon to beat the game (I didn't, on my first playthrough), you will need to delve into the upgrading system if you plan on embarking on the harder Cie'th Stone missions.
Personally, I find the upgrading system convoluted and a little unnecessary, but once you get the hang of it, it's not too bad. There are a couple of guides on GameFAQs, but like most GameFAQs guides, they overcomplicate the process.
So here's the deal. You've got a weapon — let's say Lightning's Hauteclaire — at level 1. You want to level it up to its max level, level ★. The way upgrading works is that you have component parts you have to combine with the weapon. There are a lot of components, but all we really care about are the best, cheapest ones that will give us the best multiplier. One of these is the Sturdy Bone. 36 Sturdy Bones, combined with any item, will immediately give the weapon a 3x EXP bonus.
Now you have a Hauteclaire with a 3x EXP bonus. Synthetic components give the most EXP, and a base-level weapon like the Hauteclaire needs about 50,000 EXP to get from level 1 to level ★. Take what synthetic components you have on hand, like the Ultracompact Reactor and the Particle Accelerator, and combine it with your Hauteclaire. Because it already has a 3x EXP bonus, you will get the most bang for your buck.
As soon as this combination is done, though, you'll lose that 3x EXP bonus, and you'll have to use another 36 Sturdy Bones to get there. (Alternatively, you can use 24 Otherworldly Bones for the same effect.)
Now you have a Hauteclaire level ★. The Hauteclaire's next stage is the Durandal, and you'll need a Uraninite to transform your Hauteclaire level ★ into a Durandal level 1. Once you do that, you need to repeat the process all over again in order to get a Durandal level ★. You'll need a Trapezohedron to transform your tier-2 weapon into its ultimate form... better start killing turtles.
Sometimes, you just need to grind. There are a couple of really good grinding areas in the game to take advantage of.
There's a group of five Zwerg Metrodroids in the Clock Tower area hanging out by the Treasure Sphere containing the Healer's Staff. If Sazh and Vanille aren't levelled up enough for the upcoming boss fight, spend some time here — fighting these enemies is quick and easy, and nets you 640 CP per battle. To respawn them, run back to the Treasure Sphere in the Mall area.
The Barthandelus fight is a pain in the ass. Whatever party you're using, make sure it's fully levelled before you head down to meet him; you will regret it otherwise. The final area before you meet him has lots of enemies, and while it's a bit of a pain to run back and forth between them, at least there's a big selection. The outdoor areas are good for grinding as well.
The Behemoth King and Megistotherian fighting near the northeastern exit (towards Mah'habara) are too busy with each other to notice you. You'll get a preemptive strike every time you interrupt them and a base 6,600 CP. Head to the save point and run back to respawn them.
My personal favorite spot to grind is in Mah'habara, in the Maw of the Abyss area. Take the path to the level, towards the Juggernaut, and fight all of the enemies. Go far enough in to trigger the Juggernaut, but restart the battle and he'll be back behind his door and the enemies will have all respawned. A full circuit of this loop will get you 22,400 CP.
In the final area of the Tesseracts, you can fight the Wladislaus, Jabberwocky, and Bandersnatch again. This is the only time in your playthrough you'll have a chance to fight these enemies repeatedly, and you should take advantage of it, beceause for about 10-20 minutes of battle you'll net over 100,000 CP. Take an hour or two and completely max out your main party in their default roles, max your backup characters in whatever roles you want for them, and you're well on your way for an excellent postgame experience. Take my word for it: there is no better levelling opportunity than this time right here.
Personally, I save every single Deceptisol I can from the entire playthrough for this grinding period; it's worth it to make fighting the Wladislaus with the Sanctum Templar on the stairs a very easy enemy.
Remember that Adamantoise in Eden? Now you're strong enough to fight it. You can fight the ones on the Archlyte Steppe too, but I prefer the one in Eden because you can immediately respawn it by saving and reloading at the point right there, or by running back and forth to the door to Edenhall. (Running to the door is quicker.) You get 40,000 CP per battle, and will need to fight it for Trapezohedrons anyway. Its common drop is Platinum Ingots, an easy source of gil.
I suggest this guide; it does take some time to get strong enough, and at first it will take multiple staggers, but eventually you'll be able to use the first deck listed there to beat it in about 2 minutes every single time.
Having played the game through twice, I have a couple of tips to impart to improve your gameplay experience.