。
She wants to be a designer.
Literal
She [topic-は] designer [to-に] [wants to-become-なりたがっている].
Stacks three pieces. ~になる ('become X') is the basic change-of-state pattern. ~たい ('want to') attaches to the verb stem to express desire. ~たがる converts the first-person ~たい into the third-person desiderative — Japanese restricts directly attributing want-states to others, so for a third party you observe outwardly via ~たがる ('seems to want, wants (as observed)'). The final ~ている marks the wanting as an ongoing, sustained state rather than a momentary impulse. デザイナー is a loanword from English.