Here the phrases "eager expectation" and "certain hope" mean basically the same thing. Paul uses them together to emphasize how strong his expectation is. AT: "I am completely convinced" (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]])
These words are emphatic. They indicate that this is Paul's personal experience.
# to live is Christ
Here pleasing and serving Christ is spoken of as Paul's only purpose for living. AT: "to go on living is an opportunity to please Christ" (See: [[rc://en/ta/man/translate/figs-metaphor]])
Here death is spoken of as "gain." Possible meanings for "gain" are 1) Paul's death will help spread the message of the gospel or 2) Paul will be in a better situation. (See: [[rc://en/ta/man/translate/figs-metaphor]])