Naturally, the first 5 Cie'th Stone missions are the easiest of all and can be defeated before you finish the main story. I also strongly suggest you do just that if you want to go for an easy 5-star rating on each mission.
Each battle has a target time. Come very close to the target time and you get a 3-star rating. This means you have to win the battle before you even come close to the target time.
However, the target time is determined by your party's strength/magic and general progress. If you finished the main story -- and happily spent your well deserved CP to further upgrade your party's abilities -- the target time for weak enemies is (ridiculously close to) impossible to beat without shrouds or a preemptive strike (which isn't always possible).
I started "Mission 05: Joyless Reunion" when I finished the main story and almost completed my 10th Crystarium Expansion on each party member.
My opponent was an "Edimmu", with a target time of 27 seconds. Obviously I was way stronger than the Edimmu and it only took three gauge loads to kill it (about 21 seconds in total). That, however, also killed the time I was "actually supposed" to finish the battle and received a 3-star / 4-star rating instead.
No matter which formation I used (relentless assault, aggression, etc.) the 5-star rating was just out of reach. I was only able to achieve the 5-star rating with a Decepticol shroud that obviously resulted in an instant stagger and a fast kill. In this case, due to the Edimmu's location, a preemptive strike was not possible without the use of a Decepticol.
The 5-star rating system doesn't take the time your gauge needs to re-fill in account, and this is just a plain waste of shrouds. Especially if you don't have any, and have to purchase them at the Eden Pharmaceuticals for up to 30.000 GIL.
Note:
Yes, there is an item called Gold Watch that is obtained by defeating the last Cie'th mission, that gives you more time to earn a five-star battle. It is easier with the Gold Watch, however, it takes way more time to re-do all the Cie'th missions just for 5-stars. It's less time consuming to nail it the first time!
If you have any questions, please don't hesitate to ask!