As soon as the battle begins, change cover for a better one, behind one of the columns. Keep fighting. I strongly recommend using firearms as you won't have much time to measure your every aim.
Watch out for the enemies that will try to get close; take care of them in melee combat or with the shotgun. Notice that many of them will be wearing head covers, so not every headshot will secure the kill.
When you advance to the next part of the shootout, the game will trigger a cut-scene. Step back as far as you can from the flames so that you had more room to maneuver and be able to change covers if needed. Attack the "regular" enemies first.
Leave the armored sword-wielder for last. Same as with other encounters of this type, dodge first, then use the opportunity to fire the shotgun (reward: 140 XP).