。
She demanded an outrageous sum from me.
Literal
She [topic-は] me [from-に] outrageous amount [object-を] demanded came.
途方もない is a compound i-adjective combining 途方 ('a way, a course') + も + ない — etymologically 'lacking a way / a course,' it has come to mean 'extraordinary, preposterous, outrageous, absurd.' Often used for amounts, distances, time spans, or anything that exceeds reasonable bounds. 要求してきた is 要求する ('to demand') + ~てくる, where ~てくる marks the action as directed toward the speaker — 'demanded (and came at me with it),' giving a faintly aggressive or imposing flavor. 金額 ('sum of money') is the formal term for a quantified amount, more weighty than just お金 or 金.