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Armor & Gear
Several of the the battle circle fights are hand-to-hand. The first one is easy, subsequent ones are not. The best way to win is to remember:
armor and gear. Since you won't be able to use sheilds, items and powers, your fights rely on your skills and any bonuses from armor and gear.
It is very easy to forget, for example, that your character is probably equipped for Jedi statistics: intelligence, wisdom, force, etc. You are probably wearing robes too, but you may have armor skills. Change your head gear, your gloves, your armor and your implant to maximize strength and dexterity. If you're lacking goodies, search the nearby hangers for freebies.
Cast all your force powers such as force valor, force shield, force speed, etc. then quickly enter the match. Your powers will still be in effect. This also goes for shields.
Run if Needed
Upgrade your armor with regenerative ability. When fighting melee, if your opponent is getting the upper hand and it appears you're about to lose, continue running in circles making sure not to leave the circle until you've regain some vitality, then continue your battle. This isn't the bravest of things for a battle circle, but it works.