There are 5 levels to researching the Rosie and once the 5th level is maxed out, the trophy will pop. You can take your time and photograph all of the Rosies in the game, getting good quality grades for each photo or do as I did and you can simply photograph each splicer enough times until the quality of the photos get too low and you can’t take photographs anymore and then move on to the next one.
To help you out in getting this a little faster, you can equip the Photographer’s Eye tonics which will increase the score of the photo. Photographer’s Eye you can find in the Farmer’s Market level in the Worley Winery cellar or you can buy it at a Gatherer’s Garden Station at Fort Frolic and onward.
Also if interested, here are the rewards for each level of research:
Level 1: Increased Damage
Level 2: Photographer’s Eye 2 tonic
Level 3: Increased damage
Level 4: Rosie corpses almost always contain rare invention parts
Level 5: Increased damage