This, as well as setting the difficulty, have to be done prior to beginning a New Game.
To turn Vita-Chambers off, go into Options – Gameplay Options – Disable Vita Chambers (set this to ON). Like the first Bioshock, there is an Achievement associated with beating the game without using Vita-Chambers (respawning after death). Saving is still very important though, Save as often as you can. If you have played the first Bioshock: Remastered, this will not be as difficult as beating the game on Survivor.
All the Achievements can be unlocked in a single run of the game if you play on Hard Difficulty.