Ich verstehe diesen Satz nicht völlig:
Er trat sie unverschämt unverlogen entgegen.
Is the idiom here "entgegen treten"? Does it mean to find someone to be x?
It would have to be "Er trat ihr unverschämt, unverlogen entgegen". Entgegen always uses the Dativ.
"jemandem entgegen treten" means to face someone, it's often used with adverbs like in your sentence to describe in what way it is done. So "treten" in this case is used as "to step" (I think it has the same etymological origin as "to tread").
There's also "dem Schicksal entgegen treten" which means "to face fate".