Did I hear my name?
I have an Achilles, Purple, Powder Blue, Hippo and just got a Whitetail Bristletooth...so that's five! I did have some issues with the Achilles and Purple and had to separate them and almost got rid of the Achilles. I decided to re add him though and the aggression switched to him and the Powder Blue, (they are the same family and not recommended) but it only lasted a few hours and they are all getting along again. If the aggression shows itself again I will try the mirror trick.
The best advise I can give is to keep them fed well and have separate seaweed clips, (I have three now) so they can all eat without being in each others territory. Also have lots of hiding places in your aquascape for them to hide. If aggression does happen, don't be so quick to act and just let it play out and hopefully it stops. A few torn fins are fine among Tangs. If it gets more serious though, separation may be required.
Whatever you decide to do, good luck and post lots of pics!
Edit: I should add that I will be moving my Achilles and Hippo to a 300+ gallon tank in a couple years. For those that would tell me that a 160 gallon is not recommended for those two...yeah, I already know that.