Here "face death" means that he was in danger of dying. He knew that some people wanted to kill him because they did not like what he was teaching. Alternate translation: "Every day I am in danger of dying" or "Every day I risk my life!"
Paul uses this statement as evidence that he faces death every day. Alternate translation: "You can know that this is true, because you know about my boasting in you" or "You can know that this is true, because you know about how much I boast in you"
Paul boasted in them because of what Christ Jesus had done for them. Alternate translation: "my boasting in you, which I do because of what Christ Jesus our Lord has done for you" (See: [[rc://en/ta/man/translate/figs-explicit]])