The best way to get this achievement would be on the level where you have to secure the data boxes as Spider-Man 2099. Once you've placed all the data boxes and begin the loading sequence, you'll be swarmed by failed experiments. You have to get the 200 hits before a cutscene will show that'll immediately get rid of all of your hits. To do this, simply hit them(without getting hit, obviously) and use the special attack with LB+X(Left Button + X Button). LB+X will score lots of hits while also keeping the experiments off of you and will be more effective than RB+Y at speed. If done right you can keep going past 200 just for the fun of it.
Throughout the game you will notice some of Spidey's enemies being held as test subjects for Alchemax's projects. Such being the severed tail of the Scorpion in a test tube on the level where you chase down Anti-Venom. There is also the Sandman being held in a tube in a room behind a shielded door when you start the mission to get the Atrocity's DNA sample. There is also the future Scorpion subject being held in a test tube in 2099 as you race to save the Amazing Spider-Man.