I won’t rule out Barbara killing Penguin to avenge Tabitha or at least Barbara surviving to the end of the series, especially since her death would rule out my crackpot theory about a baby Batgirl.
If Ed and Lee hadn’t stabbed each other to (temporary) death at the end of Season 4, I’d consider perhaps Barbara and Penguin killing each other.
As of now, however, my money is much more on Barbara dying at Penguin’s hand rather than the other way around.
This is the fifth and final season, so all bets may be off about characters dying and actually staying dead.