If you're starting out on easy this shouldn't be an issue. You need to fight three Big Daddies without dying. You can use Security Bots, Turrets or hypnotize Splicers to help you take down a Big Daddy. Once you have taken down one Big Daddy save your game and move onto the next. If you are playing with the Vita Chambers off you shouldn't have to worry about re-spawning by mistake.
If you are attempting this on hard you may have a tough time taking down a single Big Daddy. Make sure you have plenty of Health and EVE, using Winter Blast with the Drill seems to be the most effective way to kill a Big Daddy. Continuously freeze him while you attack.