How do I beat the first boss (Barrett)?

Toss a yellow canister at him. Then while he's coughing and cursing you, throw one of the explosive red barrels at him.

If you're on higher difficulty levels than story mode, repeat as needed.

Very simple -- 7 non-stop zaps to the head (or 15 zaps to the body) with the Stun Gun will bring Barrett right down.

If you rush in and zap quickly enough, he won't even get a chance to shoot at you.

Run-and-gun is a pretty good strategy; I've found that weaving between the pillars tends to skew his accuracy a bit as well.

If you haven't looked already, take a glance around the two small rooms in the corners of the larger pillar room - these are chock-full of ammo and, if memory serves possibly some more grenades. You can also shoot the explosive barrels in the room to damage him.

Probably the thing that helped me the most on this fight was throwing/shooting the fire extinguishers found on the corner pillars in the room. This not only freezes him in place while he clears his eyes, but it also makes him lose you, so you can dash off to one of those corner rooms to re-stock, and then come back and shoot him in the face a bit more (I think it helps if you've upgraded your 10mm with the armor-piercing upgrade, but I couldn't swear to this, as I've never faced him without it).