You'll get this trophy for killing 500 enemies classified as Spiders. You'll know they're Spiders because the top line in the enemies name will include the phrase, example: "Spider - Phase Spiderling" (and because they LOOK like Spiders although I'm not sure whether Driders count as Drow or Spiders).
The best places to find Spiders are Rothe Valley and Ebon Downs. Ebon Downs has quite a number of spiders hanging around in groups of 3. However, outside of the village in Rothe Valley along the river you'll find spiders in groups of 5-6, specifically the small Spiderlings which are quicker to kill.
To check your progress on this trophy first press the Options button > Quests > Journal > press R1 to go to Achievements > Slayer > hit
to show them if they aren't visible and scroll down with R-stick to the Spider Slayer entries.