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