Like sacredskullkid said, the difficulty doesn't matter this time around, so play on what you're comfortable with. I got mine on normal, but you can be all fancy and go for super hard and think you're better than the rest of us or something.
Save the game all the time. Seriously, all of the time. Before you hack something, save it, before you walk through a door, save it, before you send the last Little Sister in a level through the vent (or harvest her, you evil Subject Delta you) save it. Big Sisters only attack after you've "dealt with" every Little Sister in a level, so you know when they're gonna come and you can set up the battlefield beforehand - proximity mines, trap spears, and mini turrets are your friends.
If you happen to have full health and eve, and full first aid and eve hypos, save the game, 'cause who knows when you'll see more, right?
I know it isn't much of a "solution," but if you save the game a lot, you'll have to re-do less if you end up dying somewhere, and that's really all that getting this achievement is about. Good luck!