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She completely tricked me into believing the story.
Literal
She [topic-は] me [to-に] that story [object-を] thoroughly believe-deeply-caused-to.
Two punchy elements. (1) まんまと ('completely, successfully' — usually in deception contexts) is an adverbial mimetic-ish word that pairs with verbs of trickery: まんまと騙す ('to trick completely'), まんまと逃げる ('to make a clean getaway'). It typically marks a successful con or a target swallowed whole. (2) 信じ込ませる is the causative of 信じ込む — a compound verb 信じる ('believe') + ~込む ('go fully into'), giving 'to firmly/wholly believe.' The causative -せる pushes that into 'to make (someone) firmly believe.' The whole sentence describes a successful deception with vivid economy.