Battle ratings are a function of time and difficulty of the battle: I don't want to sound like a Protip from a bad '80s magazine, but the surest way to get a five-star rating is to finish the battle faster. :P
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.
Avoid feral link abilities and eidolons. They can do massive damage, but all the flashy animation doesn't stop the clock. Favor fast attacks over slow ones.
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 (FF13-2). Maximize pre-emptive strikes by getting a "Great!" rating on the Mog Clock.
Cheat time (FF13). The Gold Watch accessory is killer for getting 5-star ratings: it doubles the target time.