The bad guys spawn in groups, kill the captain's troups without getting hit by him cos he's yellow and you can't hit him back. Once you've gotten rid of his group he'll go red and you can kill him. Multiple groups spawn in the town with different captains, choose your target.
I didn't get on too well with my tamer, but others have. I have done best using my warrior and jousting assassins and rogues. I avoid the warrior types. I suspect that a mage would do quite well against those. Some towns you can pull them far enough from the buildings that you can cast summons, but they will eventually bounce back. Challenge then is finding your target and getting him seperated without pulling a lot of other captains you don't want. Watch for the message that the beacon is vulnerable then go cast on that - be careful though because it will be surrounded by spawn. It doesn't go down in one attack, takes (I think) three attempts, with it going back 'invul' in between. Killing the beacon can also get you a minax drop.
Luckily the artifact exchange mechanism is destined to stay in game after the invasions stop.
So far I have 4 minax arties.