When you start, you will have the Wrench and the Electric Bolt Plasmid. Using 
these in rapid succession against most Splicers can often result in an 
efficient, quick kill. First, shock the Splicer. Before the convulsion ends, 
switch to the wrench, aim high, and hit the Splicer over the head. An efficient 
way of killing the Spider Splicers is to shoot a few clips of anti-personnel 
ammunition, preferably from the machine gun.