You must make it to the end of the stated
wave in order for that objective to be complete. If the scenario ends before that
wave, the objective is not considered to be completed. Objectives that state when the scenario ends, however, may be completed even if the scenario is ended before the final
wave. Note that as long as the game ends in the stated
wave, no matter the reason, unless a loss condition is triggered, that is considered the end of that
wave. For example, in Brawnen Chapter 1, Ignition, the first two listed objectives both require certain heir spires to be defeated at the end of
Wave 4. However, the third objective of defeating the heir
fortress gate can cause the scenario to end before
Wave 4. If you were to
defeat the heir
fortress gate in
Wave 3, you would not have made it to
Wave 4, and therefore would be unable to complete objectives 1 and 2, even if all the relative spires were already defeated. If you were already in
Wave 4 and ended the
wave early by defeating the heir
fortress gate, then it would count as the end of
Wave 4, meaning objectives 1 and 2 could then be completed if you destroyed the relevant spires.