사랑을 얻기 위해서라면 목슴 아나라 무엇인들 못 걸겠는가! (목슴 아나라 -> 목숨 아니라)
=> (literal) If it is to attain love, wouldn't you wager everything, not sparing even your life!
=> To attain love, wouldn't you be ready to give anything, including life itself!
When 무엇 (or 뭐) is connected with a conjugation form of all-inclusive reference such as -인들, -이든, -이라도, -이나, etc. it means "anything" or "everything". So if the phrase takes a negative question form as here (못 ... -는가), it is like "would/could one NOT do ANYTHING?", which is a rhetorical question implying "would do anything/everything".
아니라 also works similarly. It doesn't signify the usual simple negation but adds an emphasis, like "NOT JUST 목숨 BUT EVEN everything (무엇인들)". 목숨 아니라 might seem illogical because 목숨 is obviously the most important thing, but it is usually phrased this way to make it even more forceful, in the sense that if there was something more important than life, you would give it up too. For example, 내일 폭우 아니라 하늘이 두 쪽이 나더라도 떠나야 한다, "I must leave tomorrow even if the sky splits in two, let alone heavy rain".