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