In order to obtain this trophy, you need to get all 30 left arms throughout the game.
Officers with left arms can be seen immediately by initiating augment mode - their left arms pulse a green diamond.
There are rewards for obtaining all the left arms:
Wig A = 10 left arms + Completing the game on Normal Difficulty
Wig B = 20 left arms + Completing the game on Normal Difficulty
Blade Mode Wig = 30 left arms + Completing the game on Hard Difficulty
Armor Breaker (epic blade) = 30 left arms (difficulty doesn't matter).
Below is a video by Somewhat Awesome Games, and it is fantastic. If you get a chance, go give his video a thumb's up on youtube.
Also, note that Left Arm #18 only becomes available by taking out the security panels without being detected in Chapter 4 - a heavy armored cyborg will appear near the third panel once you get the first two done in a very stealth-like manner.
Questions, corrections and neg vote justifications below.