Well, I beat Left Fin + Right Fin + Sinspawn Genais + Sin Core this morning. It's actually not all that hard, here is how it works:

Left Fin

>>Enter Tidus, Yuna, Wakka
>>Left Fin does nothing
>>Tidus fakeswitches
>>Yuna summons Anima
>>Anima uses Haste on self
>>Anima uses Pain on Left Fin (about 5000 damage)
>>Occasionally Left Fin will attack for about 1300 damage
>>In this case Anima uses Cure two times on self
>>Repeat until dead

Right Fin

>>Enter Tidus, Yuna, Wakka
>>Right Fin does nothing
>>Tidus fakeswitches
>>Yuna summons Anima
>>Anima uses Haste on self
>>Anima uses Pain on Left Fin (about 5000 damage)
>>Occasionally Right Fin will attack for about 1300 damage
>>In this case Anima uses Cure two times on self
>>Repeat until dead

Sinspawn Genais

>>Enter Tidus, Yuna, Wakka
>>Genais uses venom (Kills one member)
>>This turn will result in the two remaining members having turns in a row, the second turn must be Tidus or Wakka
>>First turn swaps for Rikku
>>Rikku mixes Trio of 9999
>>Tidus uses Slice and Dice or Wakka uses Attack Reels (Overkill)

Sin Core

>>enter Tidus or Wakka, and Rikku
>>Rikku uses Al Bhed potion
>>Tidus or Wakka fakeswitches
>>Sin Core uses Gravija
>>Repeat until Tidus or Wakka has their overdrive again
>>Tidus uses Slice and Dice or Wakka uses Attack Reels (Overkill)

As I suspected, Inside Sin is incredibly incredibly tough. Maybe longer a distance than Mt. Gagazet. There is a few mob groups that will almost indefinately kill you in one turn, some that definately will. So you have to go the entire length managing not to fight them. It's possible, but it's going to be difficult as all hell.