Battle ratings are directly related to battle points, which are a function of your battle performance over the time it took to complete a battle. The Final Fantasy Wikia has the full formula analysis, and in a nutshell:
(e is a single enemy, p is a single party member)
But more basically,
- Completing the battle faster increases points.
- Taking on enemies that outmatch you increases points, while taking on enemies you outmatch decreases it1.
Since you want to maximize the number of five-star ratings you get, the enemy strength part of the formula (HPenemy and Levelenemy) are going to be constants. And unlocking ATB meter segments doesn't have an undo, so let's assume that's constant as well.
So, to maximize your points (and thus the frequency at which you get five-star battle ratings) you have two options:
- Decrease your party's combined attack power (FF13)
- Decrease the time you take to complete a battle
Decreasing your party's combined attack power (FF13)
This is easy: wield poor-quality weapons. Some battles this is pretty effective, others not so much, where you'll find the battle takes longer due to the lack of attack power.
Decreasing the battle duration
There are a few things you can do to complete a battle faster:
Invest in haste/ATB rate gear. Faster ATB gauge filling allows for more attacks per minute
Research the weaknesses of the opponents you're fighting. Check the bestiary and focus your attacks on what they're weak in.
Stagger quickly. Use paradigms like Relentless Assault (RAV, RAV, COM) to fill up the chain gauge as fast as possible. If you have three excellent ravagers, using Tri-disaster (RAV, RAV, RAV) to stagger might be a gamble, but should be doable if you outmatch your opponents. Items with quick-stagger will also help with this.
Maximize damage after stagger. Because the chain bonus from stagger is so large, it's almost always better to switch to a commando-heavy paradigm, like Cerberus (COM, COM, COM) or Aggression (COM, COM, RAV) after the stagger instead of continuing to build up the chain bonus with ravagers.
Single-target DPS difficult opponents first, then AoE everything else. Make use of the "cross" and "wide" paradigm modifiers (FF13-2) to switch between paradigms that focus fire heavy opponents (or healers) first, then take out the rest with wide attacks.
Get preemptive strikes. Maximize pre-emptive strikes by getting a "Great!" rating on the Mog Clock (FF13-2). Besides getting a head start on the battle, pre-emptive strikes increases your points by 20%, so it's definitely something you want to do often.
Cheat time (FF13). The Gold Watch accessory is killer for getting 5-star ratings: it increases the target time by 10%.
Cheese your opponents (FF13-2). Because target time is not affected by your party's strength in Final Fantasy XIII-2, most of the time you can secure five-star ratings by overmatching your opponents by expending more CP or buying better equipment.
Utilize the ATB Refresh mechanic. Due to a quirk of the paradigm shift, your ATB gauge immediately fills up when you perform a paradigm shift, allowing you to instantly execute another series of moves. You can even duplicate paradigms in your deck: for example, create two Relentless Assault (COM/RAV/RAV) paradigms next to each other so you don't have to worry about juggling ability sets. ATB Refresh has a ~10 second cooldown, though; I've been able to maximize it by doing:
- Get a preemptive strike to instantly fill up the ATB gauge
- Execute the first set of attacks
- Shift paradigms when the last attack is landing to instantly fill up the gauge again
- Execute two more sets of attacks
- Shift paradigms again to get a free ATB refill
- Go to step 4.
Note 1: Target time calculation was simplified somewhat in Final Fantasy XIII-2 and a party's power compared to its enemies no longer affects it. See my answer here for confirmation tests.