I only played through the game once on normal, but I didn't find the Big Daddies too tough. Utilize the tools you have in strategic ways.
Lay mines before you attack in a trail leading to you. If the Rosies can't see you, they'll run towards your location until they can see you. Bouncers just blitz you. Two to three mines would do a good chunk of damage, then I could widdle them down with grenades, heat seeking rockets, a machine gun with armor piercing rounds, or a shotty with electric or explosive rounds (normal shot works really well too on an upgraded shotty). Try to have these weapons upgraded, I used them the most against Big Daddies and found them and their ammo strategies most useful.
Don't forget plasmids. Winter blast is good for freezing a Bouncer in place so you can get some distance and free damage on it. Swarm is all around good for damage and keeping them busy at times. If you can, use Fury (or Frenzy, I forget it's name) to make Splicers attack the Big Daddy you are tagerting BEFORE you attack it. Target dummies can keep Big Daddies off of your back.
Don't forget to research Big Daddies with the camera as much as possible (as well as Little Sisters). Every damage bonus you can get helps.
Good luck and godspeed.
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