Hm, I would think Amaterasu would have FIR/SPI rather than FIR/MYS. I dunno, maybe Tsukuyomi could have non-elemental and spirit attacks. Or they could all have a spirit attack of some sort.
Something like...
Tsukuyomi: Time-warps, non-elemental, Spirit, and Dark attacks. Is packed with debuffs and also inflicts heavy and silence. Highly resistant to mystic, cold, spirit, and nature attacks. (Notice something?)
Amaterasu: Very powerful Fire and Spirit attacks. Also comes packed with some other elements. Doesn't really inflict status, just hits very hard. Highly resistant to fire, mystic, spirit and dark attacks. Squishiest of the 3, but is the hardest hitter of the 3.
Susanoo: Very powerful Wind and Physical attacks and an array of ways to inflict shock, terror, and paralysis. Highly resistant to wind, dark, and physical attacks. High status resistances, and also buffs his own stats often. (Kind of like Blue Giant Oni, but not 100%) Tankiest of the 3.
EDIT
So fighting Ama no Murakumo, if you fight at challenge level, it is possible for you to get a magic gem and training manual. Goodie.