After obtaining the crossbow and at least five Trap Bolts, it is easy to take down a Big Daddy. Face a wall and stand about three feet away. Make sure it is not something that the bolts can bounce off of, and also make sure you have a good ten foot long straight wall. Once you are better skilled at this technique you can try for shorter lengths if desired. Point straight ahead and fire out a bolt before taking about two steps to the left or right, depending on which way the Bid Daddy is and your location, and fire another. Fire all five bolts out, then shoot the Big Daddy once with anything. If done correctly, it will run through the line of traps, taking enough health down so he can be killed with a few shots of any other weapon. Note: This may not work in an open area because Big Daddies strafe often. If you have the damage increase for the crossbow, it will only take three or four bolts to kill him. Do not crouch while setting up the traps. If the Big Daddy walks another way and gets out of sight, you might need to go back to get him. If you do get him, you can crouch under the set traps. An easy way to trigger bolt traps is to pick up something with Telekinesis and drag the object through it.
Get your shotgun fully upgraded (power to the people stations, rate of fire, and damage upgrades) and simply use your old 00 buck. After killing them, get the Little Sister and all the money they had on them. This can result to very little damage from Big Daddies. Aim for the head to cause more damage. Note: This was done under the Easy difficulty setting.
After acquiring the Security Bullseye Plasmid, set off an alarm either by hacking or being spotted by a security camera, then throw the Security Bullseye at the Big Daddy. You may have to do this twice depending on how much health the Big Daddy has when starting out. Try to avoid the battle because the crossfire and exploding bots will damage you. The only problem with this technique is that once the Big Daddy is taken down, the bots will come after you. Be prepared to either run and hide, or fight them off.
Usually, Little Sisters will return to the same corpses several times. You can use this to your advantage by placing the corpse near a security camera with the Telekinisis plasmid, then wait for her to show up and tag her Big Daddy with the Security plasmid. He will keep returning if he survives. You can stay in the same safe location and wait for the bots to finish off the Big Daddy.
Just use two Trap Bolts in Poseidon. If you get the damage increase for the crossbow, aim for the face.