I feel like detailing a little bit how I want a battle to pan out. Right now, I am planning the Jenova BIRTH battle.

Party:
Levi
Kumo

Enemies:
Jenova BIRTH
Left Tentacle
Right Tentacle

Intended Difficulty: Tentacle RAPE. (Not really- this a moderately difficult boss battle.)

Now, since you're once again down to two party members, I'm going to not do an FFXIII and take this into consideration. BIRTH is slower than the boss fight prior to her, the Phantom, to allow for your party to get hits. You had a full party when facing the Phantom.

BIRTH can hit you with status ailments only, but she can hit you with many different ones. Blind, Slow and Silence status ailments are first introduced in this boss battle. She can also use Poison and Sleep. Levi at the beginning of the game comes equipped with Silver Glasses, which guard against Blind. The White Cape can be bought from the shop in Ghost Circle but it's up to the player to find it.
Echo Screens and Eye Drops are added to the Inventory after your finally party member, Lulu, joins up.

She can attack you as well but she has poor attack strength. Her real deadlyness comes from her lackies, the Left and Right Tentacles.
One is weak against magic but basically immune to Physical attacks. The other tentacle is the opposite. Both pull out powerful attacks like Leg Sweep and Fire/Ice/Thunder, depending on their alignment. However they're rather slow as well.

Strategy (yet to be tested):
Wipe out the magic casting tentacle with physical attacks first before aiming to disable the physical. Use Power Break on the physical tentacle to lessen its impact, and then wail away with Ice & Water.
Your MP should be running low now so restore your healer's MP with a Health Bar. Pound at Jenova with physical attacks. Only stop to remove Poison or Blind, or if your healer is Silenced to cure them with an Echo Screen.
Whatever you do, cure Poison as soon as its inflicted. If Jenova manages to Sleep both party members and then Poison one, it's good-bye for them. If she poisons both, which is unlikely, it's basically G/O.
By this point Kumo and Levi are swinging the proper Revolver and Buster Sword, so their physical attacks should be enough to finish her off with relative ease.

Once I have the enemies properly databased, I'll be testing out this strategy to its fullest extent. I'll report back in a comment on whether I had to change my strategy at all.