Since the OP did not mention 2KH, I'll address the question assuming that 2KH was not played.
If Assyrian Archer discards a hero and then plays Forgotten History, Archer is discarded. FH only forces battle resolution. It does nothing to pending triggers waiting for battle resolution.
The only reason 2KH/FH stops Archer from being discarded is because Archer's ongoing self-discard ability is interrupted by 2KH when FH forces battle resolution.
