Easy way of killing Big Daddy's:
Use 2-3 of the crossbow trap ammo on a big daddy, first line up 3 traps spaced apart in a line going across a room and then shoot the big daddy from a distance so he runs towards you. Stand where he will come for you, but go through the traps instead he will die after he hits them.
(supplied by: hitoshi-raikoh)
How to kill a big daddy on hard mode:
First make sure you have the crossbow. Then on Apollo Square find a rosie, make sure you have it fully reserched.Then take out your crossbow [also have trap bolts and lots of them] shoot like 10-15 bolts on the wall. Attack the the rosie drag it to the trap bolts, hide then let the bolts do the rest.
(supplied by: nokama)