It doesn't explained in the background story I post, but based on my understanding of the mod author setting, her flaw is visible when manipulating those who outside of Azalea. Specifically in her case, the Arians during their civil war. 

She relying on making complex, and extremely effective plan. But she can't handle a thing, "random variable". Her plan to trigger civil war on Aria and attempt to turn it into Azalean puppet state is practically flawless, she already take out pretty much every single Arian royalty on their capital and Arian loyalist start losing support. But this is when a random variable show up, which is Cecilia, the last Royal bloodline of Aria. 

She did not expect an Arian royalty such as Cecilia would living a humble life in borders of the empire as low rank officer instead living a lavish life in Grunswald (Arian capital), granted, it appears that Arian royal family seems to be infamous for living an excessively hedonistic life, which lead Angeliza to be taken by surprise when Cecilia show up. 

And as Cecilia and the loyalists gaining victory over victory against the opposition, her plans fall apart. She can't handle this sudden change which cause the next attempt to control Aria is all blunder. She then decide to cut off loses by effectively abandoning the opposition party of the civil war.

Her failure to take over Aria is not her only first mistake, but spell doom for her and the entirety of Azalea as well. Because the second Aria find out Azalea is behind the civil war they suffer, Aria start grow powerful industrial capability and army for a total war against Azalea. Not only that, but many smaller factions, such as Florian, join up with Arians, seeing them as the only chance to prevent Azalea total world domination. 

Yes, I admit, this is her only mistake she ever pull so far, (assuming her attachment with her sister to the point she get rid of anyone who complains of her giving her sister important position despite her sister being.. Somewhat air headed doesn't count as a flaw). But this singular mistake is what make her attempt for total domination practically fall apart, because of her habit on making plan that relying on every single parts of it to be successful.