so you need to kill the big daddy's
look always use the heavy stuff or weapons that you have so that they die very quickly.
then use elemental plasmids that confuse or stun big daddy like insects, ice and electric. especially electric, because that stuns big daddy's good and also damages them more then other plasmids.
after that or using simultainously use traps of any kind to make daddy's day a bit more like a living hell.
So now in a real quick way, first lay traps where the big daddy's is going to walk to damage him and slow him down. secondly use plasmids to confuse or slow the daddy and damage him even further. and finaly use your weapons wisely like use your grenadelauncher first and then continue killing him with a machinegun and finish him with a shotgun to the head.
for more fun spice things up like use fire than insects than telekinse to throw exposives at him and hitting him with a wrench and slaughtering him with a crossbow.
TOP TIP use heavy arrows with crossbow ( oohh i love that weapon and the one in Bioshock 2 ) to make him suffer a lot and put a nice arrow in his eyesocket, arms, legs, belly, back, foot, hand, mouth, neck and ass. that will make him turn in a hedgehog