Notes:
1. I encountered this issue on XBOX AND PC
2. I was playing ALONE
3. I was playing as ALL CHARACTERS
4. The achievement don't properly unlock after killing the different kind of Elite Trolls

Steps:
Finished my fourth run, one with each character, and still no achievement. Did the maps in this order to kill the necessary trolls:
Designs of the Duergar - Elite Acid Troll guaranteed in one of objectives maybe get a Elite Red Troll too.
Floating City - Red and Green Trolls, almost every time one of both types spawned as elite.
Ghosts of the Past - The Collector.
Finished every map on easiest while hunting for the first 3 troll types, leaving the collector for last as this optional boss is the only Ice Troll that appears as an Elite in the whole game.

Result:
The achievement don't unlock.

Expected Result:
Unlock the achievement.