NOTE: This is a repost after the site crash in Sept. 2010. This solution is also posted for the First Research achievement. When I first posted this solution back in February, there was already a solution for Research Master. However, all was lost after the site crash so I posted the solution here as well as First Research to ensure more people that need help can read this.
This is an easy achievement. Like McBrutalwCheese points out, you can just take a picture of the Splicer walking in front of the window of where you get the camera. It's different than in the first BioShock as this time it's a video camera and, to get the best grade, you want that camera rolling while you're in action and fighting the enemy. The deal this time is that you start rolling the film once you target an enemy with your camera and then you're free to use/change weapons/Plasmids.
Quick tips on filming:
Use combos that work best against the enemy you're fighting (e.g., Electro Bolt a Slicer and then hit it with your drill or using Armor-Piercing Rounds on a Big Daddy will net you an A+).
Change up your research tactics. If you use the same method of killing an enemy, your research points will drop (EVEN if it's an A+ combo). So once you hit that Splicer with the Electro Bolt + Drill combo a few times, Use Incinerate while they're standing in a puddle of fuel or Telekinesis + and explosive canister.
That's really all you need to know and is likely better suited for the 9 research completions achievement in the game, but I figure it's best you know it early and that achievement will come naturally if you follow the above strats.
Good luck and feel free to add your A+ combos versus certain enemies via comments (or compile a list and write your own solution) so our readers can reap the benefits.
Here's some great info by Quarantane:
"Just a note to some people, I did not finish the research for Big Sister until AFTER I had dealt with all of the little sisters. So if you deal with all little sisters and are worrying you wont see another Big Sister you need not worry, there are still a few Big Sisters (I think at least 2) to research.
I also did not finish Brute Splicer until after that point, but I believe it can be done, I think I just didn't research them well.
I went crazy when researching the Big Daddies and Big Sisters, using literally every plasmid and ammo type I could.
You should also note that there is a research bonus 1 and 2 tonic that will drastically increase your research points and there is a tonic to increase the ammount of time you can research."