If you want to complete this scene without attacking the General, you have to focus on hiding. Stay all the time in the outer part of Rotunda without getting closer to the middle and well lit arena. Lit torches may be a bit problematic for you in this task. Use Water Arrows to put them out, but don't exceed this action because they may be light again with explosive quarrels shot by the General.
To unlock the exit, you have to get to the two valves on left and right from the big locked gate (one of them is shown on the screen above). Before you start turning the particular valve, make sure that General isn't looking in your direction. If he does, he may decide to use the crossbow and hurt or even kill Garrett.
Using both valves doesn't finish the work, you have to open the door also. Before heading to this door, I recommend distract an enemy with a throwing device. As the door are very well locked, you should consider using the Focus again (if you can), what improves your lockpicking skill.