Strategy For Victory
Once you've completed Mission 03 - Massif Contamination, the Cie'th Stone for this mission will become active. After accepting the mission, your enemies location will be represented by that same pink star on the map that represents every enemy you'll be fighting during these missions. Once more, you'll have to follow the star to its location to locate the enemy. Although, this time you may have a little bit of trouble arriving at your enemies lair in one piece. The path you have to take to locate your mark sends you through a territory full of monsters that are, in all honesty, more powerful than the Edimmu you're going to face, so the best thing you can do here is just avoid them. Although, if your party needs some quick experience points before your next boss battle, depending on where you are in the story right now, these fights may be a good idea. They'll take awhile to finish, and you may take a few losses here and there, but it's all worth it in the end when you get your payoff.
After you've arrived at the lair of Edimmu, you'll realize pretty quickly that it's pretty good at evading your attacks. This isn't a huge problem, but it can be pretty annoying at times. The creature is also immune to a good deal of your physical and magic attacks, so your best bet to defeat it would be to send in a Saboteur and begin chopping away at the beast. Take note: your Commando's Ruin and Ruinga attacks are effective on the Edimmu, so that's probably what you'll want to set Lightning to use 95% of the time. The other 5% will be switching over to the Combat Clinic Paradigm and having her, along with your other medic (preferably Hope as he's the better of the two basic medics you begin with), heal the party. Speaking of medic, it's good to keep one around at all times as well, to not only heal your party after the Edimmu uses its Wind Slash, an attack that harms all three members of your party at the same time, but to cure anyone who needs it of any status ailments received via the Edimmu's Miasma ability. Combat Clinic is a very useful Paradigm to have in your pocket for when your team is getting too low on health for one medic alone to handle, so make sure you have it on your pre-set list.
A Paradigm that contains two Commando units is also a good idea, as you'll want to bring them out after you have Staggered your enemy for a quick finish. Despite it's great defense, ability to evade a good deal of your attacks, and its immunities, the Edimmu has a pretty low amount of HP when compared to a lot of the enemies you've already faced up to this point so as long as you have your Saboteur and Medic to keep things on track, losing shouldn't be an option in this situation. For defeating the Edimmu, you will receive a Sorcerer's Mark. Use it wisely. Or sell it, I could care less. Besides, it's not like it's an extremely useful item.