You'll get this trophy for killing 1000 enemies classified as Skeletons, Wights, and Zombies. You do not have to kill 1000 of each type, just a combination of the three. However, the journal will only track your kills for each enemy type up to 500.
The best places to find undead enemies are the Neverdeath Graveyard (western side) and Ebon Downs. You'll even encounter random undead sprinkled about different dungeons and adventure zones. Don't worry about grinding kills for this one because you'll likely reach your 1000th undead before finishing the Neverdeath Graveyard questline.
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 Skeleton, Wight, and Zombie Slayer entries.