This is completely self-explanatory. Any time you see a red or yellow explosive barrel, just shoot it a couple times with your pistol (so you don’t use more precious ammo types) and let it blow; just make sure you are far enough away from it when it does.
This achievement should be cumulative across the game(s). Just make sure you blow up all the barrels you see and you shouldn't have a problem. It's possible to find an area with 3-4 barrels, save, shoot them all, load, and repeat the process until the achievement unlocks, but this will likely come with regular progression without sitting through the extra loading screens.