Pattern:
宁肯 A
也不/
也要 B — 'would rather A than B' / 'would rather A and still B'. The contrast is essential —
宁肯 always pairs with
也不 (rather A than B) or
也要 (rather A in order to B). Near-synonym:
宁愿 (nìngyuàn), interchangeable in most cases.
宁肯 sounds slightly more decisive,
宁愿 more emotional.