For the Mandalorian Battle Circle, have Kreia cast self buffing abilities. The Force chain will take care of getting the Exile buffed up. If you have Lightning Gloves(1-12 electrical) or Disruption gloves(1-10 unblockable), equip them, since they add bonus damage to melee attacks, which is what you are dealing with. They won't be removed and the damage bonus helps out.
As to the Handmaiden, use a vibrosword with the best upgrades. Again, the gloves are very useful.
I always use critical strike first and keep using it during those contests.