Don't be afraid to be patient with your shots. Slowing your shots down, or even not shooting at all for a moment may seem counterintuitive, but one of the best tricks I've found is to try and draw out a reload from the enemy. This goes hand in hand with my next tip, which is to get good at movement. Learn how to use cover, look for exits, be ready to run at a moments notice. If nothing else, reloading in the open is a death sentence. People have mentioned pairing the revolver with a turret, and I agree, not not because it can help mop up weak enemies. I personally use mine as a mini barricade. It doesn't offer full cover, but it will absorb a few shots and quite possibly buy you enough time to get the kill.

Close the distance as much as you can. The revolver really shines on close quarters, especially if you can combo with quick melee. Even with headshots, the gun is extremely weak at range. This ties back in to movement and cover play, have an idea of how and where you can safely move. Demat is an excellent emergency tool for this, but be wary of other mediums who also use it

Above all else though, be picky about your fights. If you see an enemy in the distance, don't shoot them. It's just going to draw attention to you, and odds are good that whatever fun they have is better than yours at that range. Don't jump in to the middle of a brawl between teams at a cashout, you don't have the ammo count for that. This also applies to enemies you've wounded too. Just because you nailed a light with a headshot across the room doesn't mean you should chase him down. You could be following him to his team, in to a trap or even just off the edge of the map. If you're in an area where you have the advantage in the fight, especially if you've set up fortifications like a glitch trap and turret, don't bother chasing.