Here is the full list of all 15 One Troll Army achievements.
Hire 30 mercenaries.
Complete all remaining quests.
Kill the most powerful of the bosses.
Upgrade tower weapons to the maximum level.
Improve all troll skills to the maximum level.
Upgrade all buildings and towers up to level 3.
Earn 10000 materials in total.
Upgrade goblins to the maximum level.
Kill 1000 enemies.
Spend 10000 gold on resources.
Upgrade all buildings and towers up to level 2.
Earn 10000 coins in total.
Complete all buildings and towers of the fortress.
Kill 100 enemies.
Survive at least 30 waves without losses at the Survival mission.