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The first main boss you encounter in
Singularity comes about two or three hours into the game, depending on how much exploring you do before you get there. For this boss battle, you will be locked in a big room with him and there is no way out until he is defeated.
This boss phases in and out at regular intervals, and half the time he will appear and throw an explosive barrel at you. When you see the barrel coming your way, press the R3 button (click the thumbstick) to catch the barrel in mid-air, then hit R1 to throw it back at him. Once he's been hit, run around behind him and shoot the glowing spots a few times for damage. I recommend using the shotgun at close range, but you'll only get a couple of shots off before he disappears.
The key to winning this fight is to not be too close to the boss when he reappears. By keeping your distance, you can catch the barrels much more easily, but you should move in quickly to hit him from behind. Whenever he comes at you swinging his weapon, just run out of the way. I zig-zagged back and forth across the map and tried not to stay out in the open area so that I didn't get cornered. Just keep catching the barrels and shooting him until he finally goes down.