She looks shy, but she actually has a strong will.
Literal
She [topic-は] [shyly-内気に] looks [but-が], in-reality strong will's owner is.
意志の持ち主 is a stock phrase: ~の持ち主 ('owner of ~') used to attribute a quality to someone. Often paired with adjective + 性格/意志/才能/個性 — '(she) is the owner of (a quality).' Slightly literary feel. 実際は ('in reality, actually') contrasts appearance with substance.