It was her _______________ aim to bring order to the chaos, she saw all around her.

"Principal" can be an adjective meaning "main" or "most important." A "principal aim" is a primary goal. "Principle" is only a noun meaning a fundamental rule or belief, so it cannot modify "aim." "Priority" is a noun, and "important" is an adjective but doesn't convey the sense of "main" or "primary" as precisely as "principal."