Here's a helpful hint, especially when you're low on ammo or if you're trying to conserve it.

1. Get Armored Shell and Static Discharge. These are key Plasmids for this. As is Telekinesis.

2. Stock up on health and EVE vials.

3. Get the camera from Steinman (or however you spell it).

4. Research everything you can. Gaining increased damage and the Photographer's Eye 2 Plasmid (another key Plasmid). Replace Static Discharge or add this to your character.

5. With the P.E. 2 Plasmid in place, keep researching until you can't research anything else in the area.

If you do this, not only can you take down a Big Daddy in three shots with normal shotgun rounds. But you will also be able to kill Splicers with even the unlikeliest of things. Like a mask, or their hat, or even the corpse of another Splicer!