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