Familiarize yourself with toughest Arena fighters by reviewing Arena Nemeses.
Even when you use auto resolution on an Arena bout, it's possible to designate a Prime Target by just left clicking on that champion once the match starts.
Consider using this on any Revive Champions. They do resurrections. Having them out of the way early stops your champions from starting a game of "Whack a Mole"
Check out the play by play of one match to pick up some points you may have missed amid the hurly burly and chaos of battle
Consider slowing down your climb to higher Arena teams and use the easier matches to gather as much loot as possible to improve your Great Hall. You can do that by fielding a WEAK defense team and if you find that you are regularly NOT using all your bout keys take on a few no-win matches. Losses will retard your climb into tougher tiers.