This one is pretty simple. The achievement involves acquiring the video camera in Pauper's Drop and filming a research subject as you fight it by means of your weapons and plasmids until you max out the progress bar, which I believe is 4 levels. When you start filming a counter will appear on the left side of the screen, and once it is up, it will give you a score and a letter grade. Earning points fills up the progress bar of that particular subject, which you can check in your menu. You can also film a deceased subject but it won't give you near the score as a living one.
In the game, it will tell you that you need to change what you use to fight the enemy with while you're filming because doing the same thing over and over again (electrobolt - weapons) will grant you a lower score over time. So try to mix up your combos with each enemy. I personally didn't follow this rule and just used the electrobolt and a weapon and did fine throughout the campaign.
Like I said before, I believe there are 4 tiers of progress for each of the subjects and there are 9 different subjects in the game. For this particular achievement, you only need to max out one of the subjects. They are:
Thuggish Splicer - Scrounger (Allows the player to search corpses twice for different loot)
Leadhead Splicer - Thrifty Hacker (Hacked vending prices are even cheaper)
Spider Splicer - Fountain of Youth (User slowly regenerates Health and EVE when in contact with a body of water)
Houdini Splicer - Natural Camouflage (Grants invisibility when standing still for a period of time)
Brute Splicer - Armored Shell 2 (Further reduces physical damage)
Alpha Series - Elemental Storm (Causes the user to emit a burst of fire, electricity or ice at random when struck by a melee attack)
Big Daddy - Arms Race (Able to find more ammo when looting bodies and containers)
Big Sister - Drill Vampire (Successful attacks with the Drill recharge the player's Health and EVE)
Security Devices - Deadly Machines (Friendly turrets and security bots do more damage)
Each one has a tonic that is unlocked once you max out the research for it and I have included them above.