to devote oneself to; to throw oneself intoIn this construction, に marks what you devote yourself to, and 身を refers to yourself. Often used with 入れる, as in 勉強に身を入れる.
JA: もっと勉強に身を入れないと何も成し遂げられないだろうよ。
EN: You probably won’t accomplish anything unless you devote yourself more to your studies.