You'll get this trophy for killing 50 enemies classified as Trolls. You'll know they're Trolls because the top line in the enemies name will include the phrase.
I ran up 50 kills without even trying to in the mid-to-later half of the Icespire Peak adventure zone, although you can also find a few trolls in Rothe Valley under the bridges along the river by the village.
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 Troll Slayer entries.