In my opinion you should cut out the Arceus since you will almost always use Dialga's VStar ability instead of Starbirth, but if you prefer the consistency I cant blame you
Also, sidenote: since that red mana is in the reminder text for Azula, she is still a mono-black spell
It does give the opponent four life, but this downside is hardly impactful, especially considering you'll likely have a field full of creatures to take it away just as quickly as they got it
Have fun, and may you never find yourself tapped out of the color you need
Permanents entering the battlefield don't cause abilities of permanents your opponents control to trigger
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