Again, there are three trolls in the game. Obviously, you can't just ignore them, you have to seek them out to kill them. Instead of helping them you can kill them on the spot.
There is one troll in this chapter. First off, you can't just ignore him and get the achievement. You must participate in his side quest to count for the achievement. You can always find it by the ruined bridge, but just to make it easier, take the quest "Troll Trouble" on the noticeboard outside of the inn. Upon going to the troll, you will fight it a little bit, but the fight will stop when the troll's health is about halfway down. Instead of continuing the conversation, tell him that he needs to die and finish the fight (turn in the quest back in Flotsam for your reward, but it's not necessary).
Towards the end of the chapter (regardless of whose side you're on), you will encounter two trolls. The first is a she-troll being attacked by some mercenaries, so kill them. A dialogue will occur, but instead of helping her find her husband, initiate a fight and kill her. Go down the path some more to encounter her husband, who will ask you where she is. Tell him you killed her, and he will understandably fight you. Unfortunately, you will need to kill him.
Once you kill the last troll in Chapter II, the achievement will unlock.