Dark Kain is an enemy in Final Fantasy IV Advance and Final Fantasy IV: The Complete Collection. He is fought in Kain's Trial at the Lunar Ruins. He is only present in the battle for a couple turns before he uses Jump to transform into Lunar Bahamut.
Dark Kain cannot be killed by normal means, but a Tornado from Abel's Lance can do the trick. However, the Grimoire LB to summon Lunar Bahamut is dropped by Lunar Bahamut, not Dark Kain. Thus killing Dark Kain before he transforms means the player will not receive the Grimoire, and will also be unable to re-enter Kain's trial.