And there is even more!

-Defeat 100 enemies with Cait Sith.
-Defeat Roso with Cait Sith.
-Defeat Azul with Cait Sith.
-Defeat Azul Beast form with Cait Sith.

And maybe there is more.
*shudders in compulsive Kitten Sith fan glee*

How...do I unlock these missions?

Edit: The reason Kitten Sith's mog didn't become repaired is because it ate Gackt and got a massive case of indigestion. He was beyond repair.