Continue taking pictures of Spider Splicers until you have maxed out the research. The earliest you are typically able to do this is in Fort Frolic, as you will take a break from fighting the Spider Splicers during Arcadia and the Farmer's Market.
To fill the progress bar as fast as possible, take pictures of the Spider Splicers when they are fully in the frame, during an action shot (either crawling on the ceiling or attacking), and when they are with other enemies. Coupled with the 25% bonus for the Photographer's Eye tonics, you should get this early during Fort Frolic.
You must fill the research bar FIVE times, with a bonus obtained each time you fill it. The bonuses for the Spider Splicer are as follows:
1. Increased damage +
2. Spider Splicer organs can be used as First Aid Kits (extremely helpful!)
3. Increased damage ++
4. Extra Nutrition 3 (physical tonic)
5. Increased damage +++