FINAL FANTASY XIII-2

Achieve a 5 star rating in the battle versus Pacos Amethyst & Pacos Luvulite in Academia 500 AF.
The fight is the first Mission Point on the map, not to far from where you start, although to get there you have to do a small platforming section(the entire area is platforming) by waiting for the various bridges to line up so you can jump across.

During the actual fight, attempt to weaken both till they are close to death and then kill them. If you do not kill the second one fast enough he will revive the first one forcing the battle to take longer and making it harder to get 5 stars, although you can still win fast enough should he be revived to get 5 stars.

For the record, both of the other solutions already listed are perfect, I just have some quick things to add that may be helpful, especially if your party is on the weaker side and you want to get this on the first attempt:

Obsidian Medal: Defeated a powerful enemy with perfect execution:
This achievement is awarded for achieving 5 stars in the mandatory battle against Pacos Amethyst and Pacos Luvulite during your journey through the final level, Academia 500 AF. When you reach the long middle platform, this battle will start after a brief cutscene.

Enemy Stats:

Pacos Amethyst
HP: 250,400 STR: 190 MAG: 190
Weak to Fire, Absorbs Ice
Landable Status Ailments: Deprotect, Deshell, Debrave, Defaith
Unlaunchable
Employs poweful iced based attacks, revives fallen allies

Pacos Luvulite
HP: 250,400 STR: 190 MAG: 190
Weak to Ice, Absorbs Fire
Landable Status Ailments: Deprotect, Deshell, Debrave, Defaith
Unlaunchable
Employs poweful fire based attacks, revives fallen allies

Party Build:

Depending on what monsters you have available, you can switch roles, but I do recommend Noel as your main commando. My mosters at this point were: Cloudburst (RAV) Bunkerbeast (SEN) Chichu (COM)
Serah Noel Monster
Relentless Assault: RAV COM RAV
Variety: SAB MED RAV
Tri-Disaster: RAV RAV RAV
Cerberus: COM COM COM
Combat Clinic* MED MED SEN
*This is in case things go wrong..good to have a backup plan

Strategy:

For weaker parties, use a Librascope immediately upon entering battle. This will give your ravagers an early advantage in employing the right element against either opponent. Start in relentless assault and attack either beast. Switch to variety and employ deprotetect and deshell against both enemies, this will help immensly, particularly when the first goes down.

When all status ailments have hit, switch to tri-disaster and stagger the first. Once it's staggered, Relentless assault should wipe it out quickly. Now without delay, re-enter tri-disaster and stagger the second beast. Then switch to Cerberus and slam it down before it splits and regens its compatriot.

Just a note, if you're getting low on HP before you take out the first monster, use combat clinic to heal fully, then continue to destroy it. Once the first one is down you probably wont have HP issues, but if you do don't bother healing, just follow through with your attack and this achievement should be all yours!

This Achievement is: Obsidian Medal
-Defeat a powerful enemy with perfect execution
This means to gain 5 stars on the monsters
-Pacos Amethyst
-Pacos Luvullte
This monster are automatically found and fought together as they are part of the main story during Academia -500 AF-
You will know when you find this monsters because it will automatically start the fight and they look like to crystal giraffe and the fight isnt all that hard
Tactics i used:
Rav,Rav,Rav
Rav,Com,Com
Med,Med,Med
A very simple yet effective strategy

Comment on how to make this guid any better and thanks :-)