I managed to solo the "Kindred Spirits II" fight on Normal Difficulty over the weekend as BST/NIN. I'm not sure how much of a feat that is these days, but it was my first solo attempt and I figured I'd share.
Basically upon entering the SKCNM, I used a
scroll of Instant Stoneskin and
scroll of Instant Shell to help mitigate damage (purchased from the Curio Vendor Moogles). I then called Bouncing Bertha; summoned Valaineral, Lion II, Semih Lafihna and Cherukiki as trusts; equipped a
glyph axe (offhand) just long enough for my pet to build up 1000 TP; and last but not least, cast Utsusemi:Ni.
The strategy is this - rush into targeting range (thus aggroing all mobs), command Bouncing Bertha to attack the BLM, run up close to your pet (pulling all mobs together), and then use Tegmina Buffet. Voila, all mobs are focused on your pet and you are out of immediate danger. The rest of the fight is easy, as long as you make sure that (a) the BLM goes down first, and (b) you keep your pet from dealing too much damage to the SMN - you don't want Astral flow to go off early. As soon as all mobs are down except the SMN (and the elemental summon), heel your pet and drag the SMN up the stairs. Use pet food if need be, re-engage your pet on the SMN, and run out of Astral Flow range. It won't take long for the SMN to go down.
When I tried this strategy, Valaineral must've used an AOE that grabbed the attention of the elemental summon, because it followed Valaineral down the stairs while my pet was fighting the SMN. Valaineral eventually died, but there was no danger.