Hands Free Item/CollectaCard Farming
This is going to be a lot more tough than the first option. You are absolutely going to need to use the Collecta Crystarium. You will need to sink a lot of time into this to make it really viable, so be prepared to strap in and get comfortable.
The optimal setup for this will be a healer, two melee damage dealers, and one magic damage dealer. Two of these roles can only be filled by one person.
For healing, the single most efficient method of healing is by stacking Paeon skills. As there are only three characters that have all three Paeon skills, that narrows it down quite a bit. The last skill is the one that makes the decision for us. The most viable option for the final option is Soul Voice, which will double the healing effect on the healer and thus provide a huge boost to the overall healing provided. This narrowly outperforms Elegy Lv 3 and makes Cosmos the overall best healer.
We want to have a single magic user as well. This person will just stand around until the first boss enemy shows up and then will unleash a fury that will decimate several enemies in a row. Since these will basically be one shot spells, we want to make them as strong as possible. The best way to do that is to stack Bluff and Dualcast. The only character who can do that is Shantotto. You'll also want to use a scroll to teach her Ultima.
Now, the only way we'll be able to get to a boss in the first place is to be able to kill a few enemies. This is where the physical damage dealers come into play. The only way to deal damage without actually doing anything is by using Counters. There are plenty of character that can use all levels of Counter, so we will narrow the choices down further by considering what other abilities to use. The best overall ability to pair with three levels of Counter is Added Cut since it will activate each time all three Counters activate.
By looking at which characters have all three levels of Counter and also Added Cut, we narrow the choices down to four: Sephiroth, Auron, Lightning, and Paine. Of the four, Paine is the most versatile as she also has a Limit Break that deals damage on boss characters. Of the remaining three, I prefer Auron as he's also a part of my BMS team.
There are a few other characters worth consideration. Edge has the first two levels of Counter and Added Cut. His fourth ability slot can be filled with Chakra Lv 2 for added healing. Prishe has the first two levels of Counter and can fill her last two slots with any two of Chakra Lv 3, Paeon Lv 2, or The Five Lights.
Here is the current setup that I'm using:
Paine: Counter Lv 1, Counter Lv 2, Counter Lv 3, Added Cut [46 CP] or Counter Lv 2, Counter Lv 3, Added Cut, Sword Dance [59 CP]
Auron: Counter Lv 1, Counter Lv 2, Counter Lv 3, Added Cut [46 CP]
Shantotto: Dualcast, Bluff, Ultima, Ancient Magic [85 CP]
Cosmos: Paeon Lv 1, Paeon Lv 2, Paeon Lv 3, Soul Voice [87 CP]
Once you raise your overall HP high enough to survive the easier Basic stages, start boosting the Strength and Magic stats of your team. Even getting those stats into the 500 range should enable you to defeat over a dozen enemies in a stage. Pair up this strategy with the CollectaCard Groups section of the guide to find the cards that you need and efficiently farm them without any effort.