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7-4: Talk to Cid. Cutscene. Three things to do here, hit 'em up in any order you please.
Misareaux Coast: go check "Storage Compartment" on the broken down shed near the gate to Riverne. NM bugard will spawn. Hits hard but very slowly. Long battle, but if you can blink his attacks (and have someone to heal you if utsusemi drops), not hard. Has a special that removes your food effect.
Bibiki Bay: go check ??? in that little cave in the far northwest corner of the normal (not Purgonorgo) Bibiki map. NM sea monk will spawn. Hits fast but misses very consistently. Eventually uses Hundred Fists, where it misses even faster. Has sea monk attacks for AOE water damage and stat-downs. Again, long but not very hard battle.
Carpenter's Landing: go check ??? at northern corner of *eastern* CL entrance (i.e. the entrance for South Landing). NM cryptonberry (NIN) will spawn, and will promptly summon three more NM cryptonberries (BLM, SMN, and THF, and an elemental for the SMN). All have 2-hours. None of them have all that much HP, so they die pretty quickly. Cryptonberries are sleepable with Sleepga, but not very easily.
After each fight, of course, check the respective spot again. When you've seen all three cutscenes (the one in CL is mighty confusing), return to Cid for another cutscene.
7-5: Go to Sealion's Den and talk to Sueleen. Then you're ready for the next BC fight (which I have yet to win), by checking the locked gate in Sealion's Den. It's on the same airship arena as the 6-4 BC. And your opponent is ... ****** (wycialem).
Suffice it to say he has three helpers (BLM or RDM, WHM, and RNG or SAM I think, they're the Chebukki(sp?) brothers)), whom you can't hurt or disable by any means. And he can Meikyo Shisui and make what I guess could only be a level *four* skillchain called Cosmic Elucidation (for 1000+ *AOE* damage).
Oh yeah, and no level cap.