"That girl has become a beautiful woman."
Translation:Quella ragazza è diventata una bella donna.
It looks like diventare is a motion verb. For motion verbs, essere is always the auxiliary verb used in the passato prossimo. A list of 15 motion verbs is here: https://quizlet.com/130647908/italian-verbs-of-motion-flash-cards/
"Diventare" is more common, you can always use it.
"Divenire" is used less often. I wouldn't learn the cases where you can or can't use it, and would rather stick to "diventare"
Something on the topic here... http://forum.wordreference.com/showthread.php?t=549789