1:8a We do not want you to be unaware, brothers,

Brothers ⌊and sisters⌋, we (excl.) do not want you (plur.) to be unaware/uninformed
-or-
⌊Our⌋ fellow believers, we want you to ⌊clearly⌋ know

1:8b of the hardships we encountered in the province of Asia.

about how we suffered in the province of Asia.
-or-
about the big trouble which happened to us in the territory of Asia.

1:8c We were under a burden far beyond our ability to endure,

We were burdened ⌊with troubles/difficulties⌋ to the extreme, beyond our strength to cope/endure,
-or-
Excessive burdens/difficulties/hardships came upon us, which were more than we could bear/stand-against.

1:8d so that we despaired even of life.

so that we did not think we could continue to live.
-or-
It was so bad, we thought we could not live beyond them.

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