I lured the barbarians down out of the mountains, where they have a strong advantage—onto the plains. I took my army into one of the corners, away from all the rocks, hills, mountains: and they had to come after us with no terrain advantage. I also always had at least one mounted archer that could ride out, inflict damage and, at least in some cases, make it back to the main group. The barbarians were easy to pick off when they weren’t standing on rocks.
I’d send mounted cavalry and archers to inflict damage on the barbarian slingers, then get out, if possible.
Iron Age archers proved to be very successful against the barbarians, as well. I had at least two Iron Age archers in every army I fielded against the barbarians.
I had great success using mercenaries in two of the battles in that Barbarian province: I’d get my mercenaries into forests or bushes, where they have an attack advantage; I’d just keep them there until some of the Barbarians had to leave their rocks to come after them—my mercenaries took them out every time, and none of them died.