The best method for completing this achievement is using the Shotgun with Phosphorous Buck Shot. You will pick up the Research Camera in Pauper's drop, but you will not find Phosphorus Buck Shot until Siren Alley. Use any preferred method of research until you find Phosphorus Buck Shot.
One other thing that will help is the Keen Observer Tonic found in Pauper's Drop, or bought later at a Gatherer's Garden for 40 Adam.
Before starting any research, equip the Shotgun with Phosphorus Buck Shot as your weapon, then switch to the Camera. When you start the Camera, you will automatically switch back to your last equipped weapon. When you shoot the Phosphorus Buck Shot at an enemy it will stick to them and then explode a couple of seconds later. For some reason this causes your research score to increase exponentially. You will be able to achieve an A or A+ rating during each session. Using this method you should be able to complete all research before Persephone.
On thing to note is you will only research a subject until the next level, and then the Camera will stop. An example would be a Leadhead Splicer with only 200 points until the next level. This will probably only take one shot of Phosphorus Buck Shot to gain the next level, keep this in mind to conserve ammo when needed.
Have fun and enjoy Rapture's many strange inhabitants...