。
I'm struggling to make a living.
Literal
Living [for-のために] is-struggling.
奮闘 ('struggle, fight, exert oneself') is a formal/written Sino-Japanese noun, often appearing as the noun-する verb 奮闘する. It conveys more effort and intensity than simple 頑張る. Used of serious struggles — against poverty, in a competition, with a difficult task. のために marks the purpose.