Know the arena
This is one of the most important things. Even if you do not have the best weapon you can win by knowing your way around the arena. It gets harder though, when your opponent knows the arena the same or better than you do.
In arenas that are new to you
Try to remember key items, colors and architecture. Scout out a little bit of the arena at a time and be sure of your surroundings. If you start running around the players that know the level or that are better than you will have an advantage. Know where the entrances and weapons are in the area that your in. Do not be afraid to move around, but know the area that you are in and watch you radar.
Know where each gun and ammo are
One thing that will hinder you is not having ammo for your awesome weapon. This is one thing that I don't like to happen to me. I make sure I have more than enough ammo. If someone attacks me while gathering ammo, I use what ammo I have and let them have it. Don't save you ammo if your not winning a shoot-out just because you want to save up your ammo, pull out your weapon and blast away!
Find good hiding spots
One way for you to get kills is the wait for your victims. This is good when you don't really know you way around or you just want to sniper at your opponents. Find spots that have more that one entrance. If you don't you will be trapped and most likely will lose a shoot-out or at least badly wounded. You do not want to be in a spot that has more than two or three entrances. The more entrances most of the time means more traffic. Find spots that you would not look for yourself. It would be good also to have more than one hiding spot.
Learn where your opponents like to stay
This will help you most when looking for a good weapon. Many times your opponent will like to hang around a certain place or places. By avoiding your opponents you can easily get the weapon and ammo of your choice. If the area that they like the stay in has the good weapon, try to find the next best one. Or you could distract them and draw them away from the area, allowing you to run in and get the weapon and ammo. This is sometimes hard to do.
Know your weapons
You need to know how to use some of the weapons, if not most of them. You would have better success by knowing how to use, say the Mauler then if you were using the Slayer and did not know how to use it. Even though the Slayer is more deadly it depends on you knowledge of each weapon. Your knowledge of weapons is one of the determining factors on if you win a shoot-out.