If I may contribute some technical nitpicking:
It appears the Big Daddy alone occupies all eight sprites at its widest point, meaning there will be massive flickering between that row, the same row on the player, and the projectile. Assuming there is no overlapping, it uses up two or three of the four color palettes. The little sister shares one of those palettes, but the player character uses two sets of completely different colors. I suggest you use the same browns palette from the Big Daddy on the player. I haven't checked the background...
Depending on how much it moves (I haven't played Bioshock), you might consider making (most of) the Big Daddy out of background tiles, where the only hard limit on size would be the amount of memory used. You would loose the ability to change palettes every 8x8 tile though.
Of course, you don't have to consider any of this, but it can cause your picture to 'look wrong' to people familiar with NES games. Also, observing hardware limits on palettes can lead to better use of colors as a side-effect.