BioShock

Take pictures of every Rosie that you see.
Use as many photography enhancing Tonics as you can.
Try to take action shots, such as a Rosie charging at you.
If you do this, you should get the Achievement about 75% through the game.

Also note that if you can't manage to get an action shot or find it really tough fighting the Rosie and taking pictures of it at the same time, you CAN take pictures of its dead body, however they will be worth less points.

Last note, pictures are generally worth more if other subjects are also in the shot. This is very convenient for Big Daddies since Little Sisters are often following them around. Try to get a shot of a Rosie charging at you with a Little Sister next to it - instant A+.

Courtesy of Crimson Drifter and others: "note that you will need to fill the bar 5 times for the achievement, and that you get little bonuses each time you fill the research bar." -- Thanks people!

Good luck!

Continue taking pictures of Rosies until you have maxed out the research. The earliest you are typically able to do this is in Arcadia.

To fill the progress bar as fast as possible, take pictures of the Rosies when they are fully in the frame, during an action shot (attacking, preferably another enemy), and when they are with other enemies.

You must fill the research bar FIVE times, with a bonus obtained each time you fill it. The bonuses for the Rosie are as follows:

1. Increased damage +
2. Photographer's Eye 2 (combat tonic)
3. Increased damage ++
4. Find rare invention materials on Rosie corpses
5. Increased damage +++