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]])
# to die is gain
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]])