Quite easy actually, the hardest part is finding/killing all the big daddies.
If you don't know if you've dealt with all of them in an area just pause, there will be an icon at the bottom telling you how many are in an area, the icon will be different whether you've harvested, rescued, or not dealt with the sister. If a big daddy is in the icon you haven't dealt with it.
When you find them there are some easy ways to kill the big daddies.
1) Get the hypnotize big daddie plasmid from Tenenbaum by saving some little sisters. Then find a big daddy hypnotize him and lead him to another. Attack the second and then the 2 big daddies will fight until one is dead. If it's the one you attacked then you will have to finish the job. And if it's not then the second will be an easy kill. Not only is this a good way to kill the big daddy, it is one of the most awesome minions you will ever control, and the fight is also awesome to watch.
2) Get the security bullseye plasmid (forgot how). Find a big daddy and see if you can find a camera. LEAVE THE CAMERA ALIVE, DON'T HACK IT. Then you can use security bullseye on the big daddy alert the camera and all the security bots will go after the big daddy leaving you alone. Keep repeating until the big daddy is dead. The good thing about this method is the big daddy will leave you alone after the alarm is over/
3) Equip Static discharge and stock up on electric buck and trap bolt/steel bolt. Lay some trap bolts with your crossbow spread a good distance apart that the big daddy will run into. Stay on the opposite side of your trip bolts and alert the big daddy, then try and use your crossbow and kill him before he gets to you, if he does get close use your electric buck. Shoot and then wait for him to start moving and shoot again this will keep him stunned and may give you enough time to reload a shell. Hopefully he dies before he gets close, but if he does hit you static discharge should stun him.
EDIT: This tip is mainly for the "Drill" big daddies, for the ones with the rivet gun you should use one of the other tips.
Some general tips:
1) ALWAYS make sure the little sister is with the big daddy, otherwise you have no real reason to kill it.
EDIT: If you see a Big Daddy without a little sister, but haven't gotten all of them in the area follow the Daddy to a vent and there is a chance he will call a sister from the vent. Leave some distance when you're following it, if you're to close he will not grab the sister.
2) The crossbow does a lot more damage than you may think and is actually your best bet at long range, use it to your advantage. Not only that but the trap bolts will also do massive damage and will stun him for a short time.
3) ALWAYS do your research photos before you kill it. You can take several photos and if he's near the little sister you can get close for an action shot/multiple subject bonus. The research will drastically increase your damage done.
4) If you have completed your research equip the plasmid that increases research damage. (this will help with any other enemy you have researched as well.)
5) Remember to pause and make sure you've dealt with the little sisters in the area before you leave. Although you can come back later it will be hard to remember which areas to go back to, and dealing with them while your there is much easier.