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