A fistful of lightning is probably all you'll need. That and the ability to shoot bees from out of your hand. The wrench is a great weapon here. Combine with sneaking and wrench lurker tonic and you've got yourself a winner.
Haven't tried it on hard though. In my playthrough (medium), I only had difficulty at the beginning. Ammo and money was scarce, and the first Big Daddy encounter was really a balls-to-the-wall experience. By the time I got near the end, everything I invented got doubled (hack tools, ammo, etc.) and my coffers were always full. As for Big Daddies: Shock, then incendiary rounds to the face. Lather, rinse, repeat until dead.