Here the word "expectation" and the phrase "hope" mean basically the same thing. Paul uses them together to emphasize how strong his expectation is. Alternate translation: "I eagerly and confidently hope" (See: [[rc://en/ta/man/translate/figs-doublet]])
The phrase "my body" is a metonym for what Paul does with his body. This can be stated in active form. Possible meanings are 1) "I will honor Christ by what I do" or 2) "people will praise Christ because of what I do" (See: [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-activepassive]])