Originally Posted by GoGoScoop
On my "Brass Balls" runthrough, I took out the first Big Daddy by circling around the "bar" area where you encounter him. In the middle of that area there's a column/pillar of sorts with a bar on one side of it. I used electric buck and basically shot/stunned him while circling that (to use it as cover).
I took down first Big Daddy by throwing at him gas containers i found in this level. Before battle i collected them in one place. It enough with 4 containers to kill Big Daddy on hard difficulty.